The Dominion EstablishedFootnote ¹

Beginning in 1675 King Charles II launched a general attack on many English charters, domestic and colonial, in an attempt to centralize control of his empire (Haffenden Reference Haffenden1958). In 1684 the charter of the Company of Massachusetts Bay was revoked. After Charles's death in 1685, his brother James II united Massachusetts with neighboring colonies in the Dominion of New England. He appointed a president and council that had absolute local authority on all legislative, executive, and judicial matters (Batchellor Reference Batchellor1904, vol. 1, pp. 93–99).

The absence of an elected assembly was highly unusual for an established English colony under royal control. Throughout the colonial period, it generally happened only in young colonies and those recently occupied from foreign powers, such as Jamaica and New York (Labaree Reference Labaree1930, pp. 175–77, 270n, 423). The absence of an assembly in New England surely reflected James's ideas on government that would get him deposed in England (Pincus Reference Pincus2009, chap. 6), although he did allow Bermuda (which also lost its charter in 1684) to retain its assembly (Dunn Reference Dunn1963). It is thus possible that the absence of assembly in the Dominion was also in part because James saw the runaway hardline Puritan colonies almost as occupied enemy territory. Puritans in England deposed and executed the king's father Charles I, and the New England colonies gave refuge to two regicides. Keeping an eye on New England had been a major reason for occupying a neighboring Dutch colony which became James's private colony (New York). After the occupation, James and his officials sometime treated Massachusetts as an enemy (Ritchie Reference Ritchie1977, chap. 1 and pp. 112–13).

The commission James II sent to the president was in fact the constitution of the Dominion, as in all English royal colonies (Labaree Reference Labaree1930, chap. I). It stated that the president was to lead the council temporarily, until a governor would arrive. The first role listed in the commission was the administration of justice, explicitly including land cases. Appeal to King-in-Council was limited to cases involving significant sums. The president appointed was a young politician named Joseph Dudley. Dudley was a member of the local elite by birth, a former magistrate at the Massachusetts General Court, and a former agent of the colony in London.

The Bank

London of the early 1680s saw a few failed attempts to create a land bank (Horsefield Reference Horsefield1960, chap. 10). The plan was for a bank to accept mortgages on people's lands and give in return a loan in banknotes issued by the bank itself. The Bank of England did not exist yet, and a land bank was supposed to relieve shortage of coin. From contemporaries to Douglass C. North and Barry R. Weingast (Reference North and Weingast1989), it has been the conventional wisdom that large-scale banks could not arise in Stuart England because of the bad reputation of the Stuarts as gross violators of private property rights. Notable and traumatic examples were the confiscation of merchants' deposits at the Tower of London in 1640 and a huge default on government debt in 1672. One of the participants in a failed land bank project was a financier named John Blackwell. In late 1684 he immigrated to Boston. His past as Oliver Cromwell's Treasurer-at-War made him popular enough to nearly be elected to the Massachusetts General Court upon arrival.Footnote ²

Seventeenth-century English America was so chronically short of silver that it adopted the Native American seashell money and legalized the use of bullets, fur, tobacco, and grain as media of exchange. Massachusetts opened a mint but lost it in the early 1680s as part of the charter revocation (Goldberg Reference Goldberg2009). The shortage of coin hurt all sectors of the economy, including the dominant crop agriculture. Land had to be cleared from wild vegetation and animals, fenced against the colonists' pigs, and then sown with seeds. Purchase of tools, fencing materials, seeds, animals (for draft or food), and sometimes hired labor, required credit from merchants (practically but informally backed by future crops), or liquidity. Lack of liquidity in one year could have implied that the land was not exploited according to its potential and therefore lower income was derived from the land when crops ripened. Liquidity was important for expansion and other long-term investments in agricultural land. Unmaintained land was quickly taken back by nature (Rutman Reference Rutman1967, especially pp. 20–21; Konig Reference Konig1979, chap. 3).

Blackwell probably thought that a land bank could be more successful in America than in England. America had less coin. It had much more land, which had little initial value but could be improved and was freely traded. America also enjoyed a huge distance from the predatory Stuarts. The bank prospectus explicitly referred to the farmer's liquidity problem (Davis Reference Davis1910, vol. I, pp. 121–46). It offered a loan based on the farmer's mortgaged land. The bank differed from preexisting ad hoc market mortgages in being an institutionalized arrangement of long-run loans, and in that the bank issued its own money.

The bank scheme was launched right after Dudley became president in May 1686. In June the council formed a grand and standing committee of merchants, chaired by Blackwell, to discuss ways to end a recession that was blamed on England's recent closure of the mint and new enforcement of the mercantile Navigation Acts. In July Blackwell proposed his bank scheme to the council, which referred it to Blackwell's own committee. The committee approved. In September the council approved the committee's report and promised to act in favor of the establishment of the bank. Most remarkably, the council made the prospective banknotes legal tender for all debts and taxes. It is very unusual in monetary history to give such status— then generally reserved to royally minted coins of precious metal —to private banknotes. The Bank of England was approved by Parliament in 1694 only after its promoters gave up their demand that the banknotes would be legal tender (Horsefield Reference Horsefield1960, pp. 126, 146).

The bank's astonishing progress emanated from the personal involvement of the government leaders in the bank (Lewis Reference Lewis1967). Its directors were Blackwell, President Dudley, Deputy President William Stoughton, and Councilor Wait Winthrop. Stoughton was Dudley's closest friend and business partner and was appointed deputy by Dudley himself. Winthrop was a leading councilor. Two other bank officers, former colony treasurer James Russell, and the richest man in Boston, Councilor Samuel Shrimpton, were senior members in Blackwell's committee.

The symbiotic relations between the absolutist government, the trade committee, and the private bank were a “dominant coalition” (North, Wallis, and Weingast Reference North, Wallis and Weingast2009). Such relations between political and economic elites are the rule in “limited access orders”—dictatorships and immature democracies. Either the political leaders are personally involved in large business ventures and provide benefits that no truly private business can obtain, or they sabotage the projects entirely. Seventeenth-century England and its colonies were such limited access orders.

A New Governor

At the same time in England, a governor was appointed for the Dominion. Sir Edmund Andros was a soldier and a lifelong servant of the Stuarts, who had been Governor of New York in the 1670s. His commission was longer than Dudley's but the important differences had nothing to do with land (Batchellor Reference Batchellor1904, vol. 1, pp. 146–55). The Dominion was still to be ruled by the same absolutist council. Most of the text on administration of justice was copied verbatim from Dudley's commission. Andros's commission gave him more powers, reflecting its more permanent nature, such as imposing new taxes. Two other differences could have had an effect on land (but did not). First, the authority to make “acts and orders” was replaced by an authority to make “laws, statutes, and ordinances” which had to be sent to England for approval. Second, Andros was “to agree with” the colonists, with the “advice and consent” of the council, that lands “in our power to dispose of” be granted with quitrents. Except for the lack of an assembly, the commission was similar to those given to other royal governors. Andros's powers were based on the king's prerogative in England and on the idea that he personally represented the king in the colony (Labaree Reference Labaree1930, chaps. I, III). He also received private instructions that authorized him to “dispose of” land “for which our royal confirmation may be wanting” (Batchellor Reference Batchellor1904, vol. 1, pp. 155–67). Dudley became Andros's deputy.

In December 1686 Andros took office. In May 1687 he made his friend John West land registrar and began attacking land titles.Footnote ³ He said that all land titles were defective and invalid for the following reasons: the lands reverted to the Crown upon the charter's revocation, Natives were not eligible to sell land, towns were not incorporated and thus could not grant lands, and the grants were not sealed. Presumed land owners had to petition him for a survey of the land and confirmation of the title. This land policy was part of a general disrespect of property rights, which extended to the common rights of towns (Barnes Reference Barnes1923; Martin Reference Martin1991, chap. 9). Andros also let Anglicans into a Puritan church and the Puritan college (Harvard).

Andros was able to do all that to English subjects because they were, in some sense, occupied by England. It was normal for colonies to surrender peacefully in return for a guarantee of preexisting property rights. Examples include royalist Virginia in 1651 (Hening Reference Hening1823, vol. I, p. 364) and New Amsterdam in 1664 (Ritchie Reference Ritchie1977, p. 22). In contrast, Massachusetts did not surrender its charter peacefully but went to battle in court. It thus failed to obtain a confirmation of property rights. Its situation was not much better than Spanish Jamaica that was occupied on the battlefield (1655) and lost all property rights.Footnote ⁴ The deviations of Massachusetts land law from English land law had no excuse (as the Dutch of New Amsterdam obviously had), no ex-post blanket confirmation, and—under Andros—no forgiveness. Andros's lack of good faith is proven by the fact that he unnecessarily invalidated all titles, even though most of them had gone undisputed for decades. While they were perfectly legal according to local land law, as far as English land law was concerned most colonists had only de facto possession of lands. His behavior was consistent with the absence of assembly that was typical of occupied foreign colonies.

Andros was slow in implementing his wholesale repudiation of land titles, probably fearing a revolution or recall from the king (Barnes Reference Barnes1923, p. 188; Toppan and Goodrick Reference Toppan and Goodrick1909, vol. VI, p. 206). He started giving land to his cronies, leading to numerous legal disputes. He made no law other than prohibiting future purchases from Natives. Legislating about past titles might have been seen as unjust retroactive action, and would have had to be sent to England for approval. It was safer to keep everything in the judicial arena. Although Dudley was chief justice, the attorney general could appeal his decisions to the council which was under Andros's control.

The bank partners thus had time to react. They understood that the appointments of Andros and West were a “shock to the dominant coalition” in the terminology of North, Wallis, and Weingast. There were two ways to deal with it: beat them or join them. Elisha Hutchinson, a bank partner, land developer, and merchant, went to lobby in London against Andros, trying to get him recalled or have his policy changed. Councilor Richard Wharton, the biggest Massachusetts land developer, tried the same. Dudley, however, apparently thought the shock could be handled by making Andros a partner in the bank. Nothing came out of this attempt (Davis Reference Davis1907).

Andros knew the power of merchants' lobbying in London. That is what got him recalled from New York (Ritchie Reference Ritchie1977, chap. 5) and got the Massachusetts charter revoked a few years earlier. He had to wait until he got a hint of the king's opinion. In July 1688 he received a new commission which did not rebuke his land policy and even gave him New York and New Jersey (Batchellor Reference Batchellor1904, vol. 1, pp. 226–34). Andros saw this as an implicit approval. One week later, the emboldened Andros launched an unprecedented legal attack, prosecuting some of the colony's elite for supposedly invading the king's land. The attack was prepared by the new attorney general James Graham, another friend of Andros. Graham threatened that all the rich would be targeted for all their lands. Four days after the prosecution started, as a record number of colonists rushed to petition for confirmation of their land titles, Blackwell announced that the bank scheme was aborted because the partners wished to withdraw (Goldberg Reference Goldberg2011). Four months later, the Glorious Revolution in England deposed James II. In April 1689 the colonists revolted and arrested Andros, Dudley, West, Graham, and others.

It is important to note that what Andros did regarding land was also feasible for Dudley to do. The differences in their commissions were irrelevant since Andros used the judicial arena (rather than the legislative arena) and there they had the same powers. This fact brings forth a critical puzzle: why did two dictators under virtually the same absolutist constitution treat the same financial venture in so drastically different ways within just two years? One joined, headed, and promoted the bank plan, while the other did not join and destroyed the validity of the land titles—the asset upon which the bank was based. The next section will point a possible source for such starkly different policies.

Dudley the Local

Joseph Dudley was born in Massachusetts in 1647.Footnote ⁵ His father Thomas was the second most important founder, serving four times as governor and founding Cambridge. Due to his ancestry, Joseph was elected at age 27 to the General Court. In 1681 he was sent to London to defend the Massachusetts charter from revocation. It was a hopeless battle, as mentioned above. Due to their religious mission in America, most Massachusetts leaders preferred political martyrdom to surrender. Dudley and another agent were instructed not to agree to any change in the charter.

Dudley, however, was aware of recent events in New Hampshire, which was a de facto Massachusetts county. In 1679 Dudley had been appointed by the Massachusetts General Court as a judge in New Hampshire. Soon he lost this job as the king took over New Hampshire and appointed there a president, a council, and an assembly (Batchellor Reference Batchellor1904, vol. 1, pp. 1–8). In the British Isles, “president” was a provincial administrator, as in Wales and Munster, somewhat lower than a governor. The commission to the president recognized the colonists' rights to the land due to their long possession and improvements. The president and councilors were of the local elite and had been chosen by the colonists to petition England against independence from Massachusetts (Belknap Reference Belknap1831, vol. 1, p. 86). The king probably tried to buy their loyalty with honors and salaries. With these elites on board, nobody else could oppose the Crown. Without them he might have to send over troops (Stackpole Reference Stackpole1916, vol. 1, p. 105). The president was John Cutt, the richest merchant in Portsmouth and a former deputy at the Massachusetts General Court. He was appointed for one year at least and then until further notice.

The form of royal government in New Hampshire was a valuable lesson for Dudley. It was the first time since 1624 that the king took over an English American colony governed by a corporation. It was the only precedent for predicting what would happen to Massachusetts if it were to lose its charter. Dudley realized that he was in Cutt's shoes: a distinguished colonist and member of the Massachusetts General Court who represented his community in favor of that Court. Dudley's mission was a golden opportunity to make himself personally known to the king. Instead of Cutt's riches, he had ancestral credentials. He was in a perfect position to become President of Massachusetts.

Dudley indeed switched sides. In England, he collaborated with the royal court in discussions on the future form of government. He supposedly showed the private instructions given to him by the Massachusetts General Court—an unusual move designed to signal a personal willingness to compromise. One royal official wrote that Dudley “has his fortune to make in the world, and if his Majesty, upon alteration of the government, make him captain of the castle of Boston and the forts in the colony, his Majesty will gain a popular man.”

Dudley returned home to hatred and verbal abuse from fellow colonists. In 1684 he was not reelected to the General Court, which was an unusual event for any magistrate, and especially for someone of such ancestry. He asked the king that the new constitution would arrive with “assurance of his people's properties.” This reflected his concerns as a major land developer. Most of the elite participated in a rush on the large tracts of land cleansed of Natives during King Philip's War (1675/76). Together with partners, Dudley owned three towns and kept buying land with his friend Stoughton, the banker Blackwell, and others. In one transaction, they bought a million acres from the remnants of a tribe. Overall, Dudley alone claimed at least 8731 acres (Lewis Reference Lewis1967).

In the meanwhile, New Hampshire's disputes with its English private proprietor led to the replacement of the local president with an English lieutenant governor. England learned there accidentally that an upgrade of royal authority can be eased by first appointing locals as president and council. It was decided to do the same in Massachusetts (Sainsbury and Fortescue Reference Sainsbury and Fortescue1896, #1413). Dudley was therefore explicitly appointed only until the arrival of a governor. His continued land purchases prove his confidence in the maintenance of property rights under the new governor. Given such confidence, there was no reason to reject Blackwell's invitation to the bank leadership. Dudley's council approved the bank in September 1686, taking into account a rumor that Andros would arrive in October (Sewall Reference Sewall1878, vol. I, p. 148). Indeed, Avner Greif predicts that “administrators who are also economic agents are more likely to implement choices leading to economic sectors that complement” their own economic interests (Greif Reference Gonzalez de Lara, Greif and Jha2008, pp. 47, 48). As a major land developer, it was natural for Dudley to promote the complementing land bank. He must have known that appointed councilors usually served for life in the English Empire (Labaree Reference Labaree1930, p. 135). As England's most favorite colonist, at the age of 39 he expected to remain in some leading position for many years to come.

Dudley indeed remained in a leading position as Andros's deputy. Trying to lead the colonists by example, he successfully petitioned Andros for confirmation of his land titles. He was appointed chief justice and casually violated the most sacred rights of Englishmen. He refused Habeas Corpus and punished colonists who refused to pay taxes that were not levied by an assembly. As a result, he was the only local man to be kept under arrest after the revolution. His business partners, relatives, and friends on the revolutionary government sent him to house arrest twice. In both times, he was quickly returned to jail by angry armed mobs, an unprecedented event in orderly Massachusetts.

To complete the picture in terms of Olson's framework, it should be noted that Dudley could not have expected to be a roving bandit. He could expect to be a leader only in Massachusetts, because there was no precedent for the English appointment of a native of one colony to the government of another colony.Footnote ⁶ The other bank leaders also descended from founding fathers of Massachusetts: William Stoughton was son of founder Israel Stoughton and Wait Winthrop was grandson of legendary Governor John Winthrop. They too could expect to stay in a social, economic, and political leadership position in the Dominion, and only there, for many years.

Andros the Foreigner

Edmund Andros was born in the island of Guernsey.Footnote ⁷ He served the royal family from an early age, in exile during the Interregnum and later in the Caribbeans. In 1674 he became Governor of New York —James Stuart's private colony. His banditry career started there. He faced many accusations of illegally profiting from his position, mostly by his control of the all-important beaver trade (Ritchie Reference Ritchie1977, chap. 5). Land titles were relatively secured from him. Dutch titles had been confirmed, and new titles had been granted, by James's previous governors. He found a legal excuse to seize only land which was not used by its owners, and the complaints which reached England proved that the legality of this was questionable. He also got into a fight with his neighbors, the New Jersey proprietors, who were James's friends (Andrews Reference Andrews1934, vol. III, p. 158). Eventually he was recalled by James in 1680. He was exonerated but was not returned to office. In 1686 James, now King James II, appointed him again to an American office.

In 1687, soon after taking office, Andros started bringing cronies from New York. The abovementioned John West and James Graham had first arrived to New York with Andros in 1680. West had been government secretary there while Graham had been attorney general. Two men joined the Dominion in 1688, demoting Dudley further: Francis Nicholson became lieutenant governor (based in New York) and New Yorker John Palmer became chief justice (Whitmore Reference Whitmore1868, vol. I, p. xx; Ritchie Reference Ritchie1977, pp. 180–81, 198). The Puritans bitterly complained about these “foreigners,” meaning Anglicans with no property in Massachusetts (Sewall Reference Sewall1878, passim; Whitmore Reference Whitmore1868, passim). Andros's first attorney general George Farewell and High Sheriff James Sherlock were recent arrivals as well (Savage Reference Savage1860–1862, vol. II, p. 147, vol. IV, p. 78).

Andros and this group probably did not expect to stay for long. The average tenure of a Stuart-appointed, post-Restoration, colonial governor was five years and the median was four and a half (see the Appendix). The probability of staying more than six years in office was only 15 percent.Footnote ⁸ Specifically, Andros himself was recalled from New York and saw frequent changes in the Caribbeans. This group could, of course, settle in Massachusetts for good, but this would not have turned them into Olson's stationary bandits. Within a few years, the king would have ended Andros's rule and he would have had the possibility of staying there only as an ordinary subject.

Geographical rotation of administrators was standard in premodern states across the world.Footnote ⁹ In France, it was mandatory. It was the main tool that kings used to prevent administrators from cultivating local loyalty and gaining independence. It was consistent with the practice of appointing foreign administrators. Empires which employed unrotated locals paid dearly: the Mongols lost Russia and the Ottomans lost control of tax collection. Rotation, just like the appointment of eunuchs and Catholic clergy, also prevented administrators from founding their own dynasties. The early English Empire had some rare long tenures (see the Appendix), but it seemed to have been unofficially recognized that rotation was important, since governors were recalled quite casually. If enough complaints arose against a governor, usually about corruption, and he had already been there for a few years, he was recalled to answer the allegations and did not return even if he cleared his name. Andros went through that himself in New York.

It is now clear why Dudley failed in getting Andros on board the bank. Such realignment of the coalition's rents would not have helped someone with as short of a time horizon as Andros. After his removal elsewhere, he would have been in the position of an absentee partner, with no ability to influence bank policy in real time and only a questionable ability to collect his share in the profits. Absentee proprietors, including the king, had a hard time collecting their rents in early America (Bond Reference Bond1919).

Dominion courts could not be expected to be too friendly to their former dictator. Moreover, the bank was supposed to handle all payments in its own paper money rather than with scarce coin, and the plan was to actively discourage repayment of its loans in coin (Goldberg Reference Goldberg2011, p. 214). Sitting in England or another colony, Andros would have had no use for the bank's notes.

This is why the realignment of power in the dominant coalition had to be more drastic—undermining the land titles of older members of the coalition, and, probably inadvertently, undermining the bank as well. Andros's second commission of 1688 implied royal approval of his realignment. Together with the joining of Graham, Nicholson, and Palmer, it shocked the dominant coalition more seriously and resulted in the bank's immediate collapse. Moreover, as a temporary administrator bent on collecting maximum short-term revenue at the expense of growth, Andros actually had an incentive to prevent “private experimentations that might reveal growth-enhancing choices” that could be made by his government (Greif Reference Gonzalez de Lara, Greif and Jha2008, p. 46).

To summarize, the situation in Massachusetts was more complicated than Olson's model of stationary and roving bandits. As an appointed dictator, Andros was expected to be in Massachusetts not for a one-day pillage but also no more than a few years; his horizon was a “closed” one. In contrast, Dudley had an “open” horizon: no effective deadline. Although as president he was very temporary, as the leading colonist he expected to maintain an ability to benefit from the colonists' lands indefinitely through a long-lived bank. One key Olsonian assumption remains intact: both dictators were egoistic. If Dudley had any patriotism, it was recognized by very few contemporaries. He was singled out as somewhat of a traitor both before and after his brief tenure as Massachusetts' first dictator. His bank and council colleagues Stoughton and Winthrop remained popular.

We now turn to formalizing the different circumstances and choices of Dudley and Andros in a model. The goal of the model is to impose some discipline on the historical analysis and to verify with the objective tools of mathematics the theoretical arguments made above. Formalizing this example also provides value for understanding other episodes.Footnote ¹⁰ The model does not intend to capture all the important details, subtleties, and complications of the case study, and indeed it could not. It only serves to examine and highlight one mechanism which we think is of paramount importance in understanding the incentives of Dudley and Andros. These two men were clearly not twins separated at birth, and they differed from each other in many ways. However, their complete identification with James's policies and style of government indicates that many of these personal differences were of secondary importance in explaining their different land policies. Their future prospects in the Dominion, however, were inherently and fundamentally different, and therefore could have been the main force at work.

Open Horizon

An open horizon means that the passing periods do not make the end of the ruler's term any closer. In other words, the probability 0 < p < 1 of at least one more period is the same in all periods, so that the number of periods has a geometric distribution with mean 1/(1 − p). This entails that investing in all periods is an equilibrium strategy for the owner. A corresponding equilibrium strategy for the ruler is δ_Ob − c to refrain from confiscating the land as long as the owner invests in it. The equilibrium payoffs are equivalent to constant payoffs of to the owner and to the ruler. Our assumption of positive net gain from investment implies that any unilateral change of strategy by the owner can only harm him. For the ruler, an effective unilateral change of strategy, which means that he confiscates the land at some point, is harmful if the gain from confiscation is lower than the expected discounted payoff from receiving in each remaining period, that is,

This inequality holds if the ruler is expected to remain in office long enough (p close to 1) and he is sufficiently patient (δ_R close to 1). Thus, in this case, the outcome that the owner always invests in his land and the ruler never confiscates it but rather facilitates the owner's investment is an equilibrium one.

Closed Horizon

A closed horizon means that the number of periods, which may or may not be known in advance, is bound not to exceed some commonly known limit N. As we show below, this limitation has a dramatic effect on the equilibrium outcome. In any equilibrium, even in mixed strategies, the ruler confiscates the land in the first period.

If the ruler is still in office in period N, equations 1 and 2 imply that his strategy must be to confiscate the land in that period with probability 1. In period N − 1, it may be optimal for the ruler not to confiscate only if he is sufficiently sure that the owner will invest in that period and he himself will still be in office in the next period, so that he can confiscate the land then. However, the owner may indeed invest only if he is sufficiently sure that the ruler will not get a chance to confiscate in the next period, an apparent contradiction. Thus, it seems that the ruler must confiscate for sure also in period N − 1.

To formalize and extend the above argument, consider any equilibrium, and suppose that there is some period such that there is a nonzero probability that the game will reach that period and the ruler will not confiscate the land then. Let 1 \le N macr \lt N be the last such period, and p macr the probability that the game will continue at least one more period, in which case the ruler will confiscate for sure in period N macr + 1. His choice not to do so in period N macr, which by the equilibrium assumption must be optimal, indicates that there is a nonzero probability that the owner will invest in period N macr and

However, for the owner, investment in period N macr is optimal only if

It is not difficult to see that this inequality and the previous one together contradict equation (2). Therefore, there cannot in fact be a period in which the ruler refrains from confiscating the land, and in particular this cannot be the case for the first period.

Confiscating the land right away gives the ruler a lower payoff than in the equilibrium in the open-horizon case (where he could do the same but chose not to), and the same is obviously true for the owner. Thus, both agents fare worse in the closed-horizon case. Significantly, this conclusion has nothing to do with the value of the limit N on the number of periods or the possibility that the game will terminate before the limit is reached. In particular, N can be arbitrarily greater than the expected number of periods 1/(1 − p) in the open-horizon case.