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.

Mis-measure of animal contests.

Contests between rivals placing similar value on the resource at stake are commonly won by the rival having greater 'resource holding potential' (RHP). Mutual assessment of RHP difference between rivals is usually expected as an economical means of resolution; weaker rivals can retreat when they detect their relative inferiority, thereby avoiding costly, futile persistence. Models of contest resolution that entail retreat decisions based on estimates of RHP difference predict that contest duration diminishes as RHP difference between rivals increases because the asymmetry is more readily detected. This prediction appears to have been fulfilled in contests of diverse taxa, generating widespread support for assessment of RHP differences in contests. But few studies have considered alternatives in which each rival simply persists in accord with its own RHP ('own RHP-dependent persistence'). In contests decided by own RHP-dependent persistence, in which costs accrue only through each rival's own actions, weaker rivals retreat first because they are inherently less persistent, and contest duration depends primarily on the weaker (losing) rival's RHP rather than RHP difference between the rivals. We show here that the analyses most commonly used to detect effects of RHP difference cannot discriminate between these alternatives. Because RHP difference between rivals tends to be correlated with RHP of the weaker rival in a pair, a negative relation between RHP difference and contest duration may be generated even when decisions of retreat are not based on estimated RHP difference. Many studies purporting to show a negative relation between RHP difference and contest duration may actually reflect an incidental association between weaker rival RHP and RHP difference. We suggest statistical and experimental approaches that may help to discriminate between effects of weaker rival RHP and true effects of RHP difference. We also discuss whether 'true' negative effects of RHP difference on contest duration always reflect retreat decisions based on estimated RHP differences. Copyright 2003 Published by Elsevier Science Ltd on behalf of The Association for the Study of Animal Behaviour.

Monoamines and decision making during contests in the hermit crab Pagurus bernhardus

During fights animals are expected to make a series of strategic decisions that involve interactions between information about the contest and the individual's nervous system that produce a change in behaviour. Biogenic monoamines such as serotonin ('5-HT') and dopamine are thought to prime decision-making centres for appropriate responses during aggressive interactions in crustaceans, and circulating levels vary both between individuals and during agonistic encounters. Aminergenic systems operate in diverse animal taxa and in this study we assayed circulating levels of S-HT and dopamine following shell fights in the common European hermit crab, Pagurus bernhardus. The two roles in these fights, attacker and defender, perform different activities but, in both, S-HT increased and dopamine declined in response to engaging in a fight. In defenders but not attackers, giving up was correlated with low 5-HT and dopamine. In attackers, motivation to initiate a fight was positively correlated with dopamine levels. Circulating monoamines are therefore involved in decision making during these aggressive encounters. (c) 2007 The Association for the Study of Animal Behaviour Published by Elsevier Ltd. All rights reserved.

Self-assessment by males during energetically costly contests over precopula females in amphipods

In animal contests, individuals can either engage in mutual assessment of both their own and their opponent's resource-holding potential (RHP) and adjust their behaviour according to estimated differences, or instead persist in accordance with thresholds determined by assessment of just their own RHP. We examined the predictions of alternative mutual assessment and self-assessment models for decision rules in contest resolution during struggles between males over females in precopula in the amphipod Gammarus pulex. Contest duration was positively related to the weight of the loser but not the weight of the winner. Our results support the hypothesis that males rely on information about their own RHP in determining contest behaviour and do not use information about their opponent. Fighting was energetically costly, and energy reserves were depleted during contests. Contest duration was associated with the physiological state of the loser (but not the winner) at the end of the contest, and to a lesser extent his size, further supporting self-assessment. (c) 2006 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.

Assessment of fighting ability in animal contests

Selection should favour accurate information gathering regarding the likely costs and benefits of continued conflict. Here we consider how variation in the abilities of contestants to assess resource-holding potential (RHP) influences fights. This has been examined in various game theory models. However, discriminating between assessment strategies has proven difficult and has resulted in confusion. To add clarity, we group existing models into three main types that differ in the information about RHP that contestants are presumed to gather: (1) pure self-assessment, (2) cumulative assessment and (3) mutual assessment. Within this framework we outline methods advocated to discriminate successfully between the three main assessment models. We discuss support for each model, before highlighting a number of conflicting and inconclusive studies, leading us to consider alternative approaches to investigate assessment. Furthermore, we examine support for newly emerging concepts such as 'varying degrees of assessment', 'switching assessment' strategies and the possibility of contestants adopting different assessment strategies within a fight involving distinctive roles. We suggest future studies will benefit by judicious use of a battery of techniques to determine how animals settle contests. Finally, we highlight difficulties with current game theory models, and raise concerns regarding the use of certain behavioural criteria to accept or reject a model, particularly since this may conflict with evidence for a given assessment strategy. Furthermore, the failure of existing models to account for newly emerging concepts points to limitations of their use and leads us to challenge game theoreticians to develop upon them. (C) 2009 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.

Information gathering and decision making about resource value in animal contests

Contestants are predicted to adjust the cost of a fight in line with the perceived value of the resource and this provides a way of determining whether the resource has been assessed. An assessment of resource value is predicted to alter an animal's motivational state and we note different methods of measuring that state. We provide a categorical framework in which the degree of resource assessment may be evaluated and also note limitations of various approaches. We place studies in six categories: (1) cases of no assessment, (2) cases of internal state such as hunger influencing apparent value, (3) cases of the contestants differing in assessment ability, (4) cases of mutual and equal assessment of value, (5) cases where opponents differ in resource value and (6) cases of particularly complex assessment abilities that involve a comparison of the value of two resources. We examine the extent to which these studies support game theory predictions and suggest future areas of research. (C) 2008 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.

Vocal rate as an assessment process during fallow deer contests

Two types of model propose that strategic decisions during contests are determined either by (i) a mutual-assessment process or (ii) a self-assessment process. Vocal signals are thought to convey information about the competitive abilities of individuals, the ultimate function of which is a reduction in costs associated with fighting consistent with the principle of mutual assessment. Nevertheless, the limited evidence that male ungulates engage in mutual assessment of vocal rates during dyadic contests has been questioned. Therefore, we examined the vocal rates of winners and losers during escalated dyadic contests between male fallow deer in order to further inform on this issue. Our results showed that winners and losers did not differ in vocal rate. The best model fit that accounted for individual vocal rates included a preponderance of factors related to the opponent indicating that contestants were attending to their opponent during fights. Vocal rate was, therefore, dependent on estimates of opponent quality without reference to self, supporting an 'opponent-only' rather than a mutual assessment process. © 2012 Elsevier B.V.

From the buzzing in Turing’s head to machine intelligence contests

This paper presents an analysis of three major contests for machine intelligence. We conclude that a new era for Turing’s test requires a fillip in the guise of a committed sponsor, not unlike DARPA, funders of the successful 2007 Urban Challenge.

Contests with the probability of a draw : a stochastic foundation

This article proposes a stochastic foundation for the contest success function (CSF for short) with a richer structure on the set of possible outcomes of the contest. Specifically, the analysis allows for the possibility of a draw, so that no contestant can claim a victory over all other players. Under plausible conditions, this article not only discovers new functional forms of CSFs, but also shows the newly derived CSFs have very different properties in equilibrium to those of conventional CSFs. For example, in contrast to the CSFs discussed in the contest literature, which always generate a unique pure strategy Nash equilibrium, the newly discovered CSFs admit the possibility of multiple equilibria.