Abstract: Gladiatorial combat was in reality a lot less lethal than it is depicted in the cinema. This short paper highlights how cooperative strategies could have prevailed in the arenas, which is generally what happened during the Games. Cooperation in the arena corresponded to a situation of the professionalization of gladiators, who been trained in gladiatorial schools. This case provides an analogy of the conditions under which cooperation occurs in a context of competition between rival companies.
Abstract: William D. Hamilton famously stated that “human life is a many person game and not just a disjoined collection of two person games”. However, most of the theoretical results in evolutionary game theory have been developed for two player games. In spite of a multitude of examples ranging from humans to bacteria, multi-player games have received less attention than pairwise games due to their inherent complexity. Such complexities arise from the fact that group interactions cannot always be considered as a sum of multiple pairwise interactions. Mathematically, multi-player games provide a natural way to introduce non-linear, polynomial fitness functions into evolutionary game theory, whereas pairwise games lead to linear fitness functions. Similarly, studying finite populations is a natural way of introducing intrinsic stochasticity into population dynamics. While these topics have been dealt with individually, few have addressed the combination of finite populations and multi-player games so far. We are investigating the dynamical properties of evolutionary multi-player games in finite populations. Properties of the fixation probability and fixation time, which are relevant for rare mutations, are addressed in well mixed populations. For more frequent mutations, the average abundance is investigated in well mixed as well as in structured populations. While the fixation properties are generalizations of the results from two player scenarios, addressing the average abundance in multi-player games gives rise to novel outcomes not possible in pairwise games.
Abstract: Costly signaling is a mechanism through which the honesty of signals can be secured in equilibrium, even in interactions where communicators have conflicting interests. This paper explores the dynamics of one such signaling game: Spence’s model of education. It is found that separating equilibria are unlikely to emerge under either the replicator or best response dynamics, but that partially communicative mixed equilibria are quite important dynamically. These mixtures are Lyapunov stable in the replicator dynamic and asymptotically stable in the best response dynamic. Moreover, they have large basins of attraction, in fact larger than those of either pooling or separating equilibria. This suggests that these mixtures may play significant, and underappreciated, roles in the explanation of the emergence and stability of information transfer.
Abstract: In repeated public good experiments, reciprocity helps to sustain high levels of cooperation. Can this be achieved by location choices in addition to making contributions? It is more realistic to rely on an intuitive neighborhood model for community members who interact repeatedly. In our experiments, participants can locate their contribution, yielding a small benefit for the participant, who receives the contribution and a small disadvantage for the participant, at the opposite location. This mechanism of individually targeted sanctions helps to foster initial cooperation. It decreases over time, however. Location choices are used to reciprocate, but may not suffice to stabilize voluntary cooperation as an effect observed in the field.
Abstract: Sponsored search advertising has grown rapidly since the last decade and is now a significant revenue source for search engines. To ameliorate revenues, search engines often set fixed or variable reserve price to in influence advertisers’ bidding. This paper studies and compares two pricing mechanisms: the generalized second-price auction (GSP) where the winner at the last ad position pays the larger value between the highest losing bid and reserve price, and the GSP with a posted reserve price (APR) where the winner at the last position pays the reserve price. We show that if advertisers’ per-click value has an increasing generalized failure rate, the search engine’s revenue rate is quasi-concave and hence there exists an optimal reserve price under both mechanisms. While the number of advertisers and the number of ad positions have no effect on the selection of reserve price in GSP, the optimal reserve price is affected by both factors in APR and it should be set higher than GSP.
Abstract: In this paper, we use a two-period one-to-one matching model with incomplete information to examine the effect of changes in divorce costs on marital dissolution. Each individual who has a nontransferable expected utility about the quality of each potential marriage decides whether to marry or to remain single at the beginning of the first period. Individuals married in the first period learn the qualities of their marriages at the beginning of the second period and then decide whether to stay married or to unilaterally divorce. We show that, for any society, there exist matching environments where the probability of the marital dissolution does not reduce divorce costs under gender-optimal matching rules. In such environments, an allocation effect of divorce costs with an ambiguous sign outweighs an incentive effect that is always negative. We also show that these results may also arise under stable matching rules that are not gender optimal.