Mutual Empathy in Games

32 Pages Posted: 29 Oct 2015 Last revised: 1 Nov 2016

See all articles by Jorge Vásquez

Jorge Vásquez

Smith College - Department of Economics

Marek Weretka

University of Wisconsin - Madison - Department of Economics

Date Written: October 29, 2016

Abstract

We investigate the effects of players’ mutual empathy, or the interdependence of players’ payoffs, on their behavior and welfare. To this end, we augment the conventional game-theoretic framework by allowing players’ utilities to depend not only on the strategy profile being played, but also on the realized utilities of other players. We call the resulting framework an empathetic game. Generally, in these games players’ utilities are not reducible to preferences over strategies due to novel feedback effects; thus, standard solution concepts, such as the Nash equilibrium, cannot be applied. We extend the notion of a Nash equilibrium to these settings by endowing players with consistent beliefs regarding others’ payoffs. We show that under mild assumptions our solution concept is well defined. We then apply the framework to analyze how mutual empathy affects strategic interactions, and find that it qualitatively changes players’ incentives. First, empathetic games can generate excessive multiplicity of equilibria owing to many supporting beliefs. Second, we uncover a new source of inefficiency, called payoff inefficiency, as players may coordinate their beliefs on socially suboptimal solutions to the interdependent payoff system. Finally, we show that these two features are common in sympathetic (altruistic) games, in which the payoffs of all players depend positively on others’ payoffs; however, payoff inefficiency never occurs in two-player antipathetic games, in which payoffs are negatively related.

Keywords: Empathy, Non-paternalistic altruism, Interdependent Payoffs

JEL Classification: C72, D64

Suggested Citation

Vásquez, Jorge and Weretka, Marek, Mutual Empathy in Games (October 29, 2016). Available at SSRN: https://ssrn.com/abstract=2681954 or http://dx.doi.org/10.2139/ssrn.2681954

Jorge Vásquez (Contact Author)

Smith College - Department of Economics ( email )

Northampton, MA 01063
United States

HOME PAGE: http://https://sites.google.com/site/jovasquez/

Marek Weretka

University of Wisconsin - Madison - Department of Economics ( email )

1180 Observatory Drive
Madison, WI 53706
United States

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