Contest Success Functions: Theory and Evidence

Contest success functions, which show how probabilities of win- ning depend on resources devoted to a conflict, have been widely used in the literature addressing appropriative activities (economics), international and civil wars (political science), and group con?ict and selection (evolutionary biology). Two well-known forms of contest success functions predict contest outcomes from the difference between the resources of each side and from the ratio of resources. The analytical properties of a given conflict model, such as the existence of equilibrium, can be drastically changed simply by altering the form of the contest success function. Despite this problem, there is no consensus about which form is analytically better or empirically more plausi- ble. In this paper we propose an integrated form of contest success functions, which has the ratio form and the difference form as limiting cases, and study the analytical properties of this function. We also estimate different contest success functions to see which form is more empirically probable, using data from battles fought in seventeenth-century Europe and during World War II. JEL Categories: C70, D72, D74Conflicts; Contest Success Functions

Is altruism bad for cooperation?

Some philosophers and social scientists have stressed the importance for good government of an altruistic citizenry that values the well being of one another. Others have emphasized the need for incentives that induce even the self interested to contribute to the public good. Implicitly most have assumed that these two approaches are complementary or at worst additive. But this need not be the case. Behavioral experiments find that if reciprocity-minded subjects feel hostility towards free riders and enjoy inflicting harm on them, near efficient levels of contributions to a public good may be supported when group members have opportunities to punish low contributors. Cooperation may also be supported if individuals are sufficiently altruistic that they internalize the group benefits that their contributions produce. Using a utility function embodying both reciprocity and altruism we show that unconditional altruism towards other members attenuates the punishment motive and thus may reduce the level of punishment inflicted on defectors, resulting in lower rather than higher levels of contributions. Increases in altruism may also reduce the level of benefits from the public project net of contribution costs and punishment costs. The negative effect of altruism on cooperation and material payoffs is greater the stronger is the reciprocity motive among the members. JEL Categories: D64 (altruism); H41 (public goods)public goods, altruism, spite, reciprocity, punishment, cooperation

Decompositions of two player games: potential, zero-sum, and stable games

We introduce several methods of decomposition for two player normal form games. Viewing the set of all games as a vector space, we exhibit explicit orthonormal bases for the subspaces of potential games, zero-sum games, and their orthogonal complements which we call anti-potential games and anti-zero-sum games, respectively. Perhaps surprisingly, every anti-potential game comes either from the Rock-Paper-Scissors type games (in the case of symmetric games) or from the Matching Pennies type games (in the case of asymmetric games). Using these decompositions, we prove old (and some new) cycle criteria for potential and zero-sum games (as orthogonality relations between subspaces). We illustrate the usefulness of our decomposition by (a) analyzing the generalized Rock-Paper-Scissors game, (b) completely characterizing the set of all null-stable games, (c) providing a large class of strict stable games, (d) relating the game decomposition to the decomposition of vector fields for the replicator equations, (e) constructing Lyapunov functions for some replicator dynamics, and (f) constructing Zeeman games -games with an interior asymptotically stable Nash equilibrium and a pure strategy ESS

Social Preferences and Public Economics: Mechanism design when social preferences depend on incentives

Social preferences such as altruism, reciprocity, intrinsic motivation and a desire to uphold ethical norms are essential to good government, often facilitating socially desirable allocations that would be unattainable by incentives that appeal solely to self-interest. But experimental and other evidence indicates that conventional economic incentives and social preferences may be either complements or substitutes, explicit incentives crowding in or crowding out social preferences. We investigate the design of optimal incentives to contribute to a public good under these conditions. We identify cases in which a sophisticated planner cognizant of these non-additive effects would make either more or less use of explicit incentives, by comparison to a naive planner who assumes they are absent. JEL Categories: D52, D64, H21. H41Social preferences, implementation theory, incentive contracts, incomplete contracts, framing, motivational crowding out, ethical norms, constitutions

Deterministic Equations for Stochastic Spatial Evolutionary Games

Spatial evolutionary games model individuals who are distributed in a spatial domain and update their strategies upon playing a normal form game with their neighbors. We derive integro-differential equations as deterministic approximations of the microscopic updating stochastic processes. This generalizes the known mean-field ordinary differential equations and provide a powerful tool to investigate the spatial effects in populations evolution. The deterministic equations allow to identify many interesting features of the evolution of strategy profiles in a population, such as standing and traveling waves, and pattern formation, especially in replicator-type evolutions

Public Goods in Networks with Constraints on Sharing

This paper considers incentives to provide goods that are partially excludable along social links. We introduce a model in which each individual in a networked society makes a two-pronged decision: (i) decide how much of the good to provide, and (ii) decide which subset of neighbours to nominate as co-beneficiaries. An outcome specifies an endogenous subnetwork generated by nominations and a public goods game occurring over the realised subnetwork. We show the existence of specialised pure strategy Nash equilibria: those in which some individuals (the Drivers) contribute while the remaining individuals (the Passengers) free ride. We then consider how the set of efficient specialised equilibria vary as the constraints on sharing are relaxed and we show a monotonicity result. Finally, we introduce dynamics and show that only specialised equilibria can be stable against individuals unilaterally changing their provision level

A classification of bargaining solutions by evolutionary origin

For games of contracting under perturbed best response dynamics, varying the perturbations along two dimensions (uniform vs. logit, directed vs. undirected) gives four possibilities. Three of these select differing major bargaining solutions as stochastically stable. The fourth possibility yields a new bargaining solution which exhibits significant nonmonotonicities and demonstrates the interplay of two key drivers of evolutionary selection: (i) the ease of making errors; (ii) the ease of responding to errors

Revenue Comparisons of Auctions with Ambiguity Averse Sellers

We study the revenue comparison problem of auctions when the seller has a maxmin expected utility preference. The seller holds a set of priors around some reference belief, interpreted as an approximating model of the true probability law or the focal point distribution. We develop a methodology for comparing the revenue performances of auctions: the seller prefers auction X to auction Y if their transfer functions satisfy a weak form of the single-crossing condition. Intuitively, this condition means that a bidder's payment is more negatively associated with the competitor's type in X than in Y. Applying this methodology, we show that when the reference belief is independent and identically distributed (IID) and the bidders are ambiguity neutral, (i) the first-price auction outperforms the second-price and all-pay auctions, and (ii) the second-price and all-pay auctions outperform the war of attrition. Our methodology yields results opposite to those of the Linkage Principle