Tit for tat: Foundations of preferences for reciprocity in strategic settings

Abstract

This paper assumes that in addition to conventional preferences over outcomes, players in a strategic environment have preferences over strategies. It provides conditions under which a player's preferences over strategies can be represented as a weighted average of the utility from outcomes of the individual and his opponents. The weight one player places on an opponent's utility from outcomes depends on the players' joint behavior. In this way, the framework is rich enough to describe the behavior of individuals who repay kindness with kindness and meanness with meanness. The paper identifies restrictions that the theory places on rational behavior.

A characterization of intrinsic reciprocity

“…Geanakoplos, Pearce, and Stacchetti [4], Rabin [5], and Segal and Sobel [6] present ways to model intrinsic reciprocity in games. These papers extend standard game theory in a way that permits preferences of one player to depend on the intentions of other players.…”

“…A tractable way to model intrinsic reciprocity is to assume, in addition, that players have strategic preferences over their own strategy set and that these preferences depend on the strategic context (or expected play of the game) so that, in particular, they need not agree with preferences over outcomes. Segal and Sobel [6] investigate this model and provide conditions under which player i's preferences over his set of mixed strategies (with representative element σ i ) conditional on a context on expected pattern of play (described by the mixed-strategy profile σ * ) is represented by a function V i (·) that can 1 Sobel [7] reviews the literature on reciprocity.…”

“…That is, depending on the strategic context, an individual can exhibit altruism (utility is increasing in opponent's material payoff) or spite (utility is decreasing in the opponent's material payoff). Segal and Sobel [6] develop this theory, provide a representation theorem, and discuss equilibrium in games with preferences for reciprocity. This paper connects the weights in equation (1) to the perceived kindness of opponents' strategies.…”

“…In order to prove the result, we introduce a Reciprocal Altruism assumption that makes precise the connection between (2) and the niceness order. Charness and Rabin [1], Rabin [5], and Segal and Sobel [6] define pref-erences over strategies in strategic-form models of reciprocity. 2 Section 3 discusses the niceness orders that are implicit in the papers of Rabin [5] and Segal and Sobel [6].…”

“…Charness and Rabin [1], Rabin [5], and Segal and Sobel [6] define pref-erences over strategies in strategic-form models of reciprocity. 2 Section 3 discusses the niceness orders that are implicit in the papers of Rabin [5] and Segal and Sobel [6]. 3 Dufwenberg and Kirchsteiger [2] and Falk and Fischbacher [3] present models of reciprocity for extensive-form games.…”