Games2015, 6(1), 2-31; doi:10.3390/g6010002 - published 9 January 2015 Show/Hide Abstract
Abstract: We study the structure of the rest points of signaling games and their dynamic behavior under selection-mutation dynamics by taking the case of three signals as our canonical example. Many rest points of the replicator dynamics of signaling games are not isolated and, therefore, not robust under perturbations. However, some of them attract open sets of initial conditions. We prove the existence of certain rest points of the selection-mutation dynamics close to Nash equilibria of the signaling game and show that all but the perturbed rest points close to strict Nash equilibria are dynamically unstable. This is an important result for the evolution of signaling behavior, since it shows that the second-order forces that are governed by mutation can increase the chances of successful signaling.
Games2014, 5(4), 234-256; doi:10.3390/g5040234 - published 14 November 2014 Show/Hide Abstract
Abstract: We investigate experimentally whether the extent of conditional cooperation in public good games depends on the marginal per capita return (MPCR) to the public good and type of game. The MPCR is varied from 0.2 to 0.4 to 0.8. The ‘standard’ game, in which three players contribute before a follower, is compared with a leader-follower game, in which one player leads and three follow. Even though we observe less conditional cooperation for an MPCR of 0.2, the prevalence of conditional cooperation remains relatively stable to changes in the MPCR and game timing. In contrast, the level of MPCR has a strong effect on unconditional contributions. Our results highlight the critical role played by leaders in a public good game.
Games2014, 5(4), 204-233; doi:10.3390/g5040204 - published 30 October 2014 Show/Hide Abstract
Abstract: This paper attacks a problem like the one addressed in an earlier work (Potthoff, 2013) but is more mathematical. The setting is one where an election is to choose a single winner from m (> 2) candidates, it is postulated that voters have knowledge of the preference profile of the electorate, and preference cycles are limited. Both papers devise voting systems whose two key goals are to select a Condorcet winner (if one exists) and to resist manipulation. These systems entail equilibrium strategies where everyone votes sincerely, no group of voters sharing the same preference ordering can gain by deviating given that no one else deviates, and the Condorcet candidate wins. The present paper uses two unusual ballot types. One asks voters to rank the candidates with respect both to their own preferences and to their discerned order of preference of the entire electorate. The other just asks voters for their own preference ranks plus approval votes. Novel mathematical elements distinguish this paper. Its Condorcet completion methods examine all candidate triples, sometimes analyze loop(s) of some of those triples, and order candidates in a set by first determining the last-place candidate. Its non-manipulability proofs involve mathematical induction on m.
Games2014, 5(4), 191-203; doi:10.3390/g5040191 - published 21 October 2014 Show/Hide Abstract
Abstract: A generalization of transferable utility cooperative games from the functional forms introduced by von Neumann and Morgenstern (1944, Theory of Games and Economic Behavior) and Lucas and Thrall (1963, Naval Research Logistics Quarterly, 10, 281–298) is proposed to allow for multiple membership. The definition of the core is adapted analogously and the possibilities for the cross-cutting of contractual arrangements are illustrated and discussed.
Games2014, 5(3), 188-190; doi:10.3390/g5030188 - published 4 September 2014 Show/Hide Abstract
Abstract: Classical economists from Adam Smith to Thomas Malthus and to Karl Marx have considered the importance of direct interdependence and direct interactions for the economy. This was even more the case for original institutionalist thinkers such as Thorstein Veblen, John Commons, and Clarence Ayres. In their writings, direct interdependence, interactions (or transactions) among agents, with all beneficial and with all problematic consequences, took center stage in economic analysis. Why, for instance, do people adhere to a particular new fashion or trend? Because others do, after eminent people, wealthy people, the “leisure class” (T. Veblen), have made it a symbol for status. The new fashion, however, ceases to serve as such a symbol once too many people follow it. The constant effort put into following trends and adopting fashion turns out to be a social dilemma, driven by Veblenian instincts, such as invidious distinction in predatory societies, conspicuous consumption and emulation. [...]