The economist and game theoretician Michael Bacharach died in 2002 before completing the present book. The book was to consist of nine chapters but Bacharach had only written four of them and drafted some materials for the rest of the book at the time of his death. The editors have written a preface to the book, a long introductory chapter, and a concluding chapter. They give a sketch of much of the material that was to be included in the unwritten chapters. They have also improved on the text of the written four chapters and used brackets to indicate their inserts. On the whole, the editors have done an excellent job in putting together Bacharach's materials. The end result is a theory of team game theory. While the book still is a torso, it does create a systematic approach purporting to show the weaknesses of classical game theory and to argue that team reasoning is needed as a remedy. The level of treatment in Bacharach's own text is not very technical and, indeed, the book is meant for a wider audience beyond game theoreticians and economists. The editors' treatments in the introduction and the conclusion are somewhat more demanding – not technically but in the sense of requiring more concentration on the part of the reader (more technical details are provided in Bacharach, Reference Bacharach1999).

The book begins by the editors' Preface describing the background of the book. In it Bacharach's plan for the book is given in some detail. This preface is a partial substitute for Bacharach's planned introductory chapter. The preface is followed by the editors' Introduction chapter that reconstructs the intended content of Bacharach's planned introductory chapter as well as his chapters on framing and coordination. In the book as it now stands, the editorial Introduction is followed by four chapters written by Bacharach, viz. The Hi-Lo Paradox (current Chapter 1), Groups (Chapter 2), The Evolution of Group Action (Chapter 3), and Team Thinking (Chapter 4), plus the editors' Conclusion.

Bacharach calls conceptual frameworks frames. The book is largely about framing related to thinking and reasoning about action. Bacharach's term is “variable frame” theory. The two basic frames in our present game-theoretic context are the “I-frame” and the “we-frame”. The two respective key questions are “What should I do?” and “What should we do?”. The answers to these questions go in terms of relevant practical reasoning, i.e. “I-reasoning” and “we-reasoning”, respectively.

Bacharach presents three types of games as puzzles for classical game theory. They are pure coordination games (or Schelling games), Hi-Lo games, and “social dilemma” games of the Prisoner's Dilemma family. Consider the following Hi-Lo game (presented in the standard way):

The big problem here is that although clearly the dominant outcome (5,5) is the one to go for, standard individualistic game theory cannot predict it. It regards the Nash equilibria (1,1) and (5,5) in a way as equally good. A player must respond by playing A if the other one chooses A and by playing B to the choice of B. There is no way to arrive at the categorical, nonconditional premise that the other one will choose A (or will choose B, for that matter). This has been known for quite some time, and various solution attempts exist in the literature. Harsanyi and Selten noticed the problem in their 1988 book and suggested that the collective principle of payoff dominance be added to the repertoire. Thus the players should accept the principle, mutually knowing that they do, and accordingly both choose A, with the desired result. In his search for a workable theory Bacharach discusses “respecification” theories, “salience” theories and “bounded rationality”. He finds these theories wanting, except for team theory (a version of bounded rationality theory). He also discusses empirical examples and experiments which seem to show a strong tendency of ordinary people to choose A in Hi-Lo. On p. 59 Bacharach introduces “reasoning in mode-P” satisfying the following two principles:

1. F1 The player ranks all act-profiles, using a Paretian criterion.

2. F2 She takes herself to have a reason to enact her component in the highest-ranked act-profile.

F1 entails collective profile ranking, where a profile of acts is an n-tuple of acts, one for each participant. In team thinking a payoff or utility function (U) – Bacharach's “payoffs” are to be regarded as utilities – is assumed to be defined over act profiles (for Bacharach, teams do objectively and literally have objectives, but they do not literally think or act, which is an odd combination). In the two-person case, mode-P reasoning recommends that a participant choose act x such that (x,y) maximizes U(x,y). In Hi-Lo, best-reply reasoning produces A if y = A and B if y = B and mode-P reasoning takes (A,A) to be the top profile (according to F1), and thus F2 yields the result that the participant chooses A if she acts rationally for the reason in question. In mode-P a player undergoes not only a payoff transformation but also a reasoning transformation (from I-reasoning to we-reasoning). No communication is needed for entering the P-mode reasoning and, in my view problematically, no “jointness” is involved here (see p. 171). The P-mode thus represents team reasoning that can take place by a mere shift from I-frame to we-frame, thus from asking the question “What should I do?” to “What should we do?”. This seems right, although it is of course appropriate to ask if there are independent reasons for the change in question, and this is something that Bacharach is looking for, and finds, later in the book.

In Chapter 2, Bacharach presents an overview of social psychological literature on groups and group identification and is especially interested in finding experimental reasons for people to identify with a group. He discusses the entification of groups from the outside and from the inside. Bacharach appears to favour an entity view of social groups (cf. below), although not much analysis is given of them or of group identification. According to him, a cardinal feature of group identification is taking the goals of the group to be one's goals and acting accordingly (p. 75).

In Chapter 2 Bacharach discusses the notions of common interest and interdependence. In a simple case, agents P1 and P2 are taken to have a common interest in joint outcome s* over s if they mutually know that both prefer s* to s. The most interesting case of common interest according to him is one where P1 and P2 can between them bring about s*, but only by an appropriate combination of acts. Here agents P1 and P2 have copower for s* over s. This notion is needed for strong interdependence as exemplified e.g. by the Prisoner's Dilemma (PD) that involves no assurance that the others will cooperate. In strong interdependence s* is not assured by individualistic reasoning in the standard game-theoretical sense. More precisely, let sol(G) be the solution set of game G and generalize the above account to concern sets of outcomes and not only single outcomes. A game G has feature I (viz. strong interdependence) if

1. (I) For some S,S* the players have common interest in, and copower for, S* over S, and sol(G) contains outcomes in S. (p. 85)

Next, Bacharach presents the following empirical interdependence hypothesis:

1. (IH) Group identification is stimulated by the perception of feature I.

If a game has feature I, individualistic reasoning cannot be relied upon to deliver a Paretian outcome s*. Feature I is possessed by social dilemmas like PD, Stag Hunt, Hi-Lo, Battle of Sexes and any bargaining game in which breakdown is a possibility. Bacharach points out that the fact that some games have feature I is the same as that individual rationality can be collectively inefficient or irrational.

In Chapter 2 Bacharach summarizes his account by emphasizing the following features: (i) we frame ourselves as members of groups, (ii) the goal of the group in this framing of self need not agree with the person's goals under her individual framing of herself, but perceived agreement of individual goals among a set of individuals favours framing as members of a group with this common goal, and (iii) the group framing tends to issue in efficient cooperation for the group goal. Together these features constitute the mechanism related to group identification (framing, common purpose, cooperation).

Chapter 3 concerns the evolution of group action. For Bacharach, the evolution of a behaviour trait such as the tendency to cooperate in a PD raises three questions: (a) Behaviour selection question: why did this trait rather than some other get selected by natural selection? (b) Production question: how is the behaviour produced within the individual (proximate mechanism)? (c) Mechanism selection question: why did this proximate mechanism evolve rather than some other that could have produced the same behaviour?

Bacharach discusses existing evolutionary evidence for the claim that human beings are cooperators and takes this claim to be well supported. By evolution here is meant biological evolution in the first place. Bacharach's claim seems to be that biological evolution did the basic job already hundreds of thousands of years ago when cultural factors only had a minor influence. His main idea is that what needs an account is humans' cooperative repertoire, the kind of repertoire for cooperation that is exhibited by cooperation in various common interest and interdependence games (e.g. Hi-Lo, PD, Stag Hunt). He mentions accounts in the literature attempting to explain cooperativeness but finds them wanting. Thus, he finds altruism and strong reciprocity as well as norms to be one-sided as explanatory factors in that they only concern the PD family of situations. For instance, altruism is not at all helpful in explaining coordination. What Bacharach takes to be needed for explanation of cooperativeness is stating a mechanism that is comprehensive (covers all common interest interactions), targeted (does not have unwanted side effects), as well as multipurpose (is a single, compact mechanism). Bacharach's own theory is based on group identification assumed to lead to intragroup cooperation in the right circumstances by transforming egoistic motivations into ones directed to group goals.

This chapter also contains a brief discussion of Price's theorem and an illustration of it for Stag Hunt. As is familiar from the literature, this theorem requires that cooperators (and coordinators, for that matter) should stick together and form teams or subgroups involving “assortative regrouping” even if cooperation may lower their individual fitness. The point is that the whole group's or population's fitness may still increase.

Chapter 4, Team Thinking, concentrates on team reasoning of some simple kinds. To begin, Bacharach says that somebody team reasons if she works out the best combination of actions for all the members of her team, and then does her part in it (p. 121). Her reason for doing her part is that it is her part in the best combination. A team is taken to be a set of agents whose behaviour is governed by a “team mechanism” taken to be a general causal process which determines at least partly what the agents do in a choice situation. (Bacharach's team mechanism is closely related to the notion of an authority system – or group-will formation system – that I present and discuss in Tuomela, Reference Tuomela1995: Chapter 4). An authority system is essentially a causal transformation function leading to a group intention. It is used in the book to characterize social groups capable of action as a unit.) The sequence of agents' possible acts are evaluated by a payoff function U. A team mechanism M has the outcome that the agents' choices make up the best profile in terms of U, which evaluates profiles in terms of a goal all the agents share.

In full-blown team reasoning the members of the team reason in terms of “we”. Bacharach's theory of team reasoning is the most comprehensive available today. (Bacharach however was not the first to discuss team reasoning. In my earlier work, e.g. in my 1984 book, I discuss simple cases of group reasoning – see in particular pp. 33–34.) Consider now Bacharach's initial schema for team reasoning from a group's point of view (Schema 3 on p. 158) and, respectively, from an individual's point of view (Schema 4 on p. 159 in Chapter 8), where S is a set of individuals that somehow is to be understood as a social group:

Schema 3: Team reasoning (from a group viewpoint)

1. (1) We are the members S.

2. (1) Each of us identifies with S.

3. (2) Each of us wants the value of U to be maximized.

4. (3) A [a profile of actions] uniquely maximizes U.

   Therefore,

5. (5) Each of us should choose her component of A.

Schema 4: Team reasoning (from an individual viewpoint)

1. (1) I am a member of S.

2. (2) It is common knowledge in S that each member of S identifies with S.

3. (3) It is common knowledge in S that each member of S wants the value of U to be maximized.

4. (4) It is common knowledge in S that A uniquely maximizes U.

   Therefore,

5. (5) I should choose my component of A.

These schemas are taken to represent valid reasoning, by which Bacharach means success rather than ordinary logical validity. I will not here comment on this issue.

The present schemas together exhibit both a change in agency and a change of reasoning as contrasted with what we have in standard, individualistic game theory. The participants here reason as a group (“we”), and this fact involves both kinds of transformations. It seems that the idea is that in premise (1) of Schema 3 “we” refers to “we considered as a group”, a group presumably in the entity sense. Such a “we” is regarded (or postulated, rather) by Bacharach as individualistically irreducible. This matter would have needed proper defence. But given this view, team reasoning can lead not only to an answer to the question “What should we do?” (cf. Schema 3) but also to “What should I do as a team member?” (cf. Schema 4). It seems to me that Bacharach's theory is otherwise rather individualistic, the present postulated strong “we” being the central element taken to make it irreducible. Furthermore, it is said e.g. on p. 141 that team reasoning leads to joint intentions. However, the above Schema (4) falls short of that without further assumptions. It seems that at least the (instrumental) “should” here must be an all-relevant-things-considered one and that if a logically valid schema is to be had also the want in premise (3) must also be an all-relevant-things-considered one.

There are other, more specific kinds of team reasoning. Among them we have restricted team reasoning where the team reasoners are mutually known to form only a subset of S while the rest are treated as a fixed “remainder”. This means that the team reasoners must reason relative to a fixed restriction. Another type of case is provided by circumspect team reasoning. In it there is some nonzero probability for each member that she is a team reasoner.

What are the good consequences that team reasoning has as contrasted with standard, individualistic game-theoretical reasoning? According to Bacharach it is needed for common interest cases involving interdependence and will lead to cooperation with respect to the Pareto-superior outcomes. Hi-Lo games were already commented on. Here Bacharach defends the hypothesis that people also tend to team reason in their case, i.e. the tendency for a player to identify with (P,U) is strong, where P is the player set and U the shared utility function. Bacharach planned to discuss other common interest cases such as PD in a later chapter. In Chapter 4 he just points out that in PD two contrary tendencies, viz. we-framing and I-framing, are or may be at work. He goes on to present some empirical evidence for the Hi-Lo case. He concludes that group identification is prone to take place in cases involving common interest and interdependence and also in some other cases such as comembership in an existing social group or even in cases like sharing a birthday.

In all, Bacharach claims that the evidence for team reasoning can be of the following kinds (pp. 145–7): (1) group identity is “logically” (definitionally) connected to team reasoning. There is both (2) anecdotal and (3) experimental evidence as well as (4) evolutionary evidence, as seen. There is still what Bacharach calls (5) transcendental evidence meaning that the team reasoning account is the most comprehensive theory available for explaining cooperation in common interest cases (p. 146).

The editors' concluding chapter attempts to reconstruct some of Bacharach's ideas and results. I will be rather short below no matter how interesting the reconstructions are. One point that the editors emphasize is that for Bacharach rationality amounts to valid reasoning (recall the above discussion). Another point that they make is that the reasoning expressed by his schemas is instrumental and not e.g. moral. Seven different schemas of practical reasoning, attributable to Bacharach, are discussed here, and some other theoreticians' views are commented on, too. The case of the Prisoner's Dilemma is elaborated. The editors show that in the context of circumspect reasoning with a certain probability of a frame “coming to a participant's mind” (p. 171) precise conditions for the agent to cooperate or defect can be given. This makes precise the point that there are two competing action tendencies involved in a PD.

The Conclusion also contains discussion of communicative cases with remarks on organizations that involve either directing by a special agent or deciding together as their decision mechanism. There is also a long discussion on the failure of backward induction, remarks on persons as teams and on resolute choice.

A general criticism against Bacharach's theory is that he, as it were, operates with two different conceptual schemes in his analysis. His formal theory is based on the conceptual framework of classical game theory although he enriches it with group utilities. As a consequence, only some aspects of instrumentally rational thinking and action “officially” are covered. The basic psychological concepts assumed are preferences, probabilities (either subjective or objective, presumably the latter in the case of identification probabilities) and acts. Still he extra-theoretically makes use of the common sense framework of agency and speaks e.g. about goals and intentions. Other important descriptive and explanatory notions that game theory basically misses are commitments and (social and other) norms. What is needed ultimately is a (team) game theory enriched by the mentioned central notions.

Bacharach's book is not a work by a philosopher and it does not present the kinds of conceptual analyses and arguments that analytical philosophers are used to nor does he construct a full-blown conceptual framework for the field in question (as Michael Bratman, Margaret Gilbert, Seumas Miller, John Searle, and myself have tried to do in their own work). For instance, Bacharach does not give the detailed classification of groups that I think is needed for getting further central results on cooperation and collective action. In my recent book (Tuomela, Reference Tuomela2007) I have distinguished between “I-mode” and “we-mode” mental states and actions and accordingly speak of I-mode groups and we-mode groups. The latter, in contrast to the former, kinds of groups are based on the members' collective construction of the groups as their groups. This involves a strong commitment-based notion of “we” of a kind that Bacharach does not have in his system. While there can be “pro-group” I-mode action as distinguished from we-mode action, this central difference – and thus the important difference between two kinds of joint action – is not treated in Bacharach's book (my 2007 book defends the importance of collective intentionality and partly also the strong kind of collective intentionality that the we-mode involves as contrasted with pro-group I-mode collective intentionality). What the exact relationship between team game theory and standard individualistic game theory is, would have warranted some more discussion. On this point, Bacharach (Reference Bacharach1999) contains some information, though: even if individuals were regarded as singleton teams, team game theory and standard Bayesian game theory (with types regarded as teams) do not coincide.

In any case, the above critical remarks do not much diminish the value of Bacharach' theory that the editors have rendered in as complete a form as they could, given that only some chapters of the book were written at the time of his death. I warmly recommend the book to readers interested in problems of collective action and, especially, in precise game-theoretical treatment.