Team games and personal decisions
by
Michael Bacharach
University of Oxford

This paper presents and applies a generalization of game theory in which the players need not be individuals, but may be teams.

A team here is not, as in the moral hazard literature, a group of individuals who play a game in which payoffs depend on the group output. Teams are players in their own right; the theory is a multi-team generalization of the Marschak-Radner theory of teams. In the unreliable team interactions (UTIs) of B99, a team consists of a set of agents. A given agent may belong to more than one team, and a random process determines in which she is active. If she is active in team m she team reasons for m. Team reasoning is a `profile-based' form of reasoning: an agent determines her action by computing a best strategy for her team, then playing her component. The payoff of a strategy for team m reflects the fact that activity in m is unsure. A UTI is behaviourally equivalent to a setup in which each team has a manager who sends an instruction to each member which may or may not arrive and is carried out if it does. A team reasoner for a team in effect simulates the reasoning of an imaginary manager of it. It is assumed that the n managers reason like ordinary players in an n-person noncooperative game; each chooses a strategy which is a tuple of messages, and the n chosen strategies form an equilibrium. A basic result is that team reasoning is not equivalent to having the group's preferences and using ordinary (best-reply) reasoning. The intuitive reason is that team reasoners face no coordination problem between Pareto-rankable equilibria.

The UTI model has great expressive power: any n-person noncooperative games is a special case with n singleton teams. An important application is to voluntary contribution problems in which each contributor may either play for the team consisting of herself or, with some probability, experience `group identification' as studied by Brewer, Dawes and others.

Another, focussed on here, is to the problem of self control. A person living T periods is modelled as a team consisting of T agents, each of whom may or may not choose as a `person reasoner', doing so just if she `identifies with herself' as discussed by Schick and others. It is shown that (i) person reasoning implies `resoluteness' - choosing an act because it is known to be part of a previously made plan; (ii) the coordinative property of team reasoning makes whole person reasoning efficient if memory is fallible; if it is not, it is efficient provided memory costs are low compared to computational costs: it saves on the latter because a person reasoner can determine her part in the person's best strategy by a simple inference from the remembered plan.

The theory of games in which players may be teams extends the boundaries of game theory, replacing the assumption that all players are monolithic and separate individuals by a more flexible structure in which subpersonal agents can aggregate to form persons and persons can aggregate to form suprapersonal agents.
Michael Bacharach (1999), `Interactive team reasoning: A contribution to the theory of cooperation', Research in Econ. 53, 117-47; http://www.economics.ox.ac.uk/research/ BREB/default.htm
Robert Sugden (1993), `Thinking as a team: Towards an explanation of nonselfish behavior', Social Philosophy and Policy 10, 69-89.

Date received: June 21, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafk-57.