Alex Possajennikov

On the evolutionary stability of altruistic and spiteful preferences

Abstract This note demonstrates that a result on evolutionary stability, presented by Bester and Guth [Bester, H., Guth, W., 1998. Journal of Economic Behavior and Organization 34, 193–209], applies under more general preference and payoff functions.

On the Stability of Evolutionary Dynamics in Games with Incomplete Information

In an interaction it is possible that one agent has features it is aware of but the opponent is not. These features (e.g. cost, valuation or fighting ability) are referred to as the agents type. The paper compares two models of evolution in symmetric situations of this kind. In one model the type of an agent is fixed and evolution works on strategies of types. In the other model every agent adopts with fixed probabilities both types, and type-contingent strategies are exposed to evolution. It is shown that the dynamic stability properties of equilibria may differ even when there are only two types and two strategies. However, in this case the dynamic stability properties are generically the same when the payoff of a player does not depend directly on the type of the opponent. Examples illustrating these results are provided.

Equilibrium selection in a merger game

Abstract A merger game is modeled as a non-cooperative simultaneous moves, exclusive membership game of coalition formation. In the three-player case in the equilibrium selected by refinements the merger is such that the participants prefer it to other mergers involving them.

On Evolutionary Stability of Spiteful Preferences

The paper analyzes under what conditions spiteful preferences are evolutionarily stable applying the indirect evolution approach. With a quadratic material payo¤ function, spiteful preferences are evolutionarily stable for a large set of parameters. It is shown that strategic substitutability or complementarity is endogenous property of the game played with evolutionarily stable preferences. Its relation to properties of the material payoff function is analyzed. Finally, it is shown that with incomplete information only selfish preferences are evolutionarily stable.

Majoritarian Contests with Asymmetric Battlefields: An Experiment

We investigate a version of the classic Colonel Blotto game in which individual battles may have different values. Two players allocate a fixed budget across battlefields and each battlefield is won by the player who allocates the most to that battlefield. The winner of the game is the player who wins the battlefields with highest total value. We focus on the case where there is one large and several small battlefields, such that a player wins if he wins the large and any one small battlefield, or all the small battlefields. We compute the mixed strategy equilibrium for these games and compare this with choices from a laboratory experiment. The equilibrium predicts that the large battlefield receives more than a proportional share of the resources of the players, and that most of the time resources should be spread over more battlefields than are needed to win the game. We find support for the main qualitative features of the equilibrium. In particular, strategies that spread resources widely are played frequently, and the large battlefield receives more than a proportional share in the treatment where the asymmetry between battlefields is stronger.

Signaling without common prior: An experiment

The common prior assumption is pervasive in game-theoretic models with incomplete information. This paper investigates experimentally the importance of inducing a common prior in a two-person signaling game. For a specific probability distribution of the sender’s type, the long-run behavior without an induced common prior is shown to be different from the behavior when a common prior is induced, while for other distributions behavior is similar under both regimes. We also present a learning model that allows players to learn about the other players’ strategies and the prior distribution of the sender’s type. We show that this learning model accurately accounts for all main features of the data.

On Delegation in Contests and the Survival of Payoff Maximizing Behavior

In two-player contests, optimal delegation involves giving the agent incentives to maximize the principals payoff while in contests with more than two players incentives will be different from the principals payoff maximization. These results are related to the evolutionary stability of payoff-maximizing preferences in the model of indirect evolution in general symmetric games, which depends on the slope of the reaction function being zero at equilibrium. Further examples of the relationship are also discussed.

Belief Formation in a Signalling Game Without Common Prior: An Experiment

Using belief elicitation, the paper investigates the formation and the evolution of beliefs in a signalling game in which a common prior on Senders type is not induced. Beliefs are elicited about the type of the Sender and about the strategies of the players. The experimental subjects often start with diffuse uniform beliefs and update them in view of observations. However, the speed of updating is influenced by the strength of the initial beliefs. An interesting result is that beliefs about strategies are updated faster than beliefs about types. In the medium run, for some specifications of game parameters, this leads to outcomes being significantly different from the outcomes of the game in which a common prior is induced. It is also shown that elicitation of beliefs does not considerably change the pattern of play.