Evolutionarily stable in-group favoritism and out-group spite in intergroup conflict
Highlights
► We study evolutionary stability in the context of conflict between groups. ► A large set of combinations of in-group favoritism and out-group spite is evolutionarily stable. ► In-group altruism and spite towards the out-group are substitutes. ► Our framework has incomplete information and type unobservability. ► The results are neither based on the “transparent disposition approach” nor on kin-selection.
Introduction
The evolution of altruism and spiteful traits has attracted considerable attention. Altruism and spite may cause actions that impose a resource cost to the respective player, and whereas altriusm benefits others, spite harms others. Altruism or spiteful behavior have been derived and explained by evolutionary arguments in the context of kin selection and inclusive fitness (Hamilton, 1964a, Hamilton, 1964b; West and Gardner, 2010 for a review), group selection (Maynard Smith, 1964, Maynard Smith, 1998, Sober and Wilson, 1998, Reeve, 2000 for discussion; Salomonsson, 2010 for a survey),1 network reciprocity (Nowak and May, 1992, Lieberman et al., 2005) and reciprocity (Trivers, 1971, Axelrod, 1984). For reviews see Lehmann and Keller (2006), Nowak (2006), West and Gardner (2010) and Marshall (2011). Altruism has received more explicit attention, but spite was also considered early on by Hamilton (1964a) (see also Gardner and West, 2004, Lehmann et al., 2006, West and Gardner, 2010).
We offer a new reason why a whole set of combinations of altruism towards members of the same group and spiteful attitudes towards members of a competing out-group is evolutionarily stable and where in-group altruism and out-group spite are substitutes for each other.2 We study a situation in which players participate in intergroup conflict. There are two groups that are fighting against each other about the division of a given amount of resources, denoted as “the prize”. Each player is a member of one of the groups and makes contributions to the fighting effort of the own group. This type of intergroup conflict and the problem of voluntary contributions to group effort is a frequent pattern in environments in which groups of lions, dogs, birds, etc. may compete with rival groups.3 Non-kin animals may also act in groups in intergroup conflict (see Clutton-Brock, 2009 for a review).4 We consider populations of finite size. This makes the consequences of a player's actions for other players' resources relevant for the player's fitness. We consider conflict as taking place not between players, but between groups. The intergroup conflict distinguishes our framework from evolutionary models of conflict between single players.5 Also, intergroup conflict generates scope for a richer type space, by which the “type” describes the behavior or the attitudes towards members of the in-group and towards the out-group where these two attitudes can differ.6
From a formal point of view, we apply a modification of the equilibrium concept of evolutionary stability that has its origins in the seminal work by Maynard Smith and Price (1973) and Maynard Smith (1974) on evolutionary game theory. We use the concept of evolutionary stability in finite populations that was introduced by Schaffer (1988).7 We consider an evolutionary game in which each state game consists of a conflict between two groups of players, in which players have potentially different types, and in which players are randomly assigned to one of the groups. We also extend Schaffer's equilibrium concept in the context of the “indirect approach,” i.e., in an environment in which individuals' hard-wired strategies are not their resource efforts, but where individuals are hard-wired with objective functions that guide their behavior and give them more flexibility in their actions.8 This yields an interpretation of evolutionarily stable effort as in-group altruism and out-group spite.
In the intergroup conflict, the own effort contributions of a player affect his fitness in several ways. First, own contributions to group effort have a direct resource cost to the player making this effort. Second, they reduce the share in the prize for the competing group and increase the share in the prize for the own group. The share decrease for the competing group is beneficial for the player, as it decreases the resources of members of the competing group. This increases the player's fitness relative to that of the members of the rival group. The increase in the share for his own group is a mixed blessing. It increases the own resources of the player. However, it also increases the resources of all other members of the own group (who did not have to bear the additional resource cost of this effort). In isolation, this latter effect makes the individual less well-off compared to the other members of the own group. Overall, a player expends more effort in the evolutionarily stable equilibrium than he would if he were to maximize his own resources only. The higher equilibrium level of fighting effort can be seen as induced by in-group altruism, by out-group spite, or by a combination of both. In-group altruism and spite towards the out-group are substitutes.
None of the existing explanations for altruism and spite apply in our framework. First, due to the random assignment of players into groups and new assignment of players in each subsequent state game, inclusive-fitness or group selection do not apply. Altruism and spiteful behavior have also been shown to be evolutionarily stable in a framework in which players can observe other players' types and where they can base their behavior in an interaction with another player on the preference type of this other player. Eaton et al. (2011) address in-group favoritism and out-group spite in such a contest framework with type observability.9 Behavior that is conditioned on co-players' types requires that other players' types are (at least partially) observable. As we make the assumption that players' types are unobservable to others, this explanation is also absent in our framework.
In the next Section 2 we characterize the state game with two rival groups. We then consider evolutionarily stable strategies in the intergroup conflict in Section 3. In Section 4 we make use of a duality property to show that these evolutionarily stable strategies can be induced by evolutionarily stable preferences that exhibit in-group altruism and spite towards members of the out-group. Then we conclude in Section 5.
Section snippets
The state game
Let a finite number 2n of players i constitute the set N of players.10 In the state game the players (who can be considered to be the offspring from the previous
Evolutionarily stable strategies
We now ask which for all is an evolutionarily stable strategy. This implies that we concentrate on the case in which the equilibrium in evolutionarily stable strategies is a monomorphism, i.e., characterized by a single effort level xE. Mutations from such a monomorphism may occur, but we restrict the types of mutations that can emerge to one single mutant type at a time. Starting from a homogeneous population in which all players follow the strategy xE, a mutant player may appear who
Evolutionarily stable objectives
We interpret (6) now asking which objective functions of players on their own and others' resources yield these resource efforts if players behave “as if” they choose their efforts in order to maximize these own objective functions. A tool we can use for this is the “indirect approach” developed by Güth and Yaari (1992). This approach provides players with a more sophisticated evolutionary strategy: the player's effort choice maximizes a given objective function.
For economic applications it
Conclusions
Behavior in line with in-group altruism together with out-group spite can be explained as being evolutionarily stable in a framework with groups fighting with each other. This result provides an evolutionary explanation for the strong in-group favoritism that is empirically well-established for groups that are in conflict with other groups. We have also seen that spite and altruism are substitutes in the functional relationship that describes the full set of evolutionarily stable objective
Acknowledgements
We thank Mukesh Eswaran, Werner Güth, Karl Wärneryd, and two anonymous reviewers for valuable comments. The usual caveat applies. We gratefully acknowledge funding from the German Science Foundation (SFB-TR-15).
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