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Dynamic Properties of Evolutionary Multi-player Games in Finite Populations

Author(s):Bin Wu -- Arne Traulsen -- Chaitanya S. Gokhale
Journal: Games
Publisher:
Abstract
| Pages: 182-199
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.

A Note on Cooperative Strategies in Gladiators’ Games

Author(s):Jérôme Ballet -- Damien Bazin -- Radu Vranceanu
Journal: Games
Publisher:
Abstract
| Pages: 200-207
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.

Fairness in Risky Environments: Theory and Evidence

Author(s):Silvester Van Koten -- Andreas Ortmann -- Vitezslav Babicky
Journal: Games
Publisher:
Abstract
| Pages: 208-242
The relationship between risk in the environment, risk aversion and inequality aversion is not well understood. Theories of fairness have typically assumed that pie sizes are known ex-ante. Pie sizes are, however, rarely known ex ante. Using two simple allocation problems—the Dictator and Ultimatum game—we explore whether, and how exactly, unknown pie sizes with varying degrees of risk (“endowment risk”) influence individual behavior. We derive theoretical predictions for these games using utility functions that capture additively separable constant relative risk aversion and inequity aversion. We experimentally test the theoretical predictions using two subject pools: students of Czech Technical University and employees of Prague City Hall. We find that: (1) Those who are more risk-averse are also more inequality-averse in the Dictator game (and also in the Ultimatum game but there not statistically significantly so) in that they give more; (2) Using the within-subject feature of our design, and in line with our theoretical prediction, varying risk does not influence behavior in the Dictator game, but does so in the Ultimatum game (contradicting our theoretical prediction for that game); (3) Using the within-subject feature of our design, subjects tend to make inconsistent decisions across games; this is true on the level of individuals as well as in the aggregate. This latter finding contradicts the evidence in Blanco et al. (2011); (4) There are no subject-pool differences once we control for the elicited risk attitude and demographic variables that we collect.

Unraveling Results from Comparable Demand and Supply: An Experimental Investigation

Author(s):Muriel Niederle -- Alvin E. Roth -- M. Utku Ünver
Journal: Games
Publisher:
Abstract
| Pages: 243-282
Markets sometimes unravel, with offers becoming inefficiently early. Often this is attributed to competition arising from an imbalance of demand and supply, typically excess demand for workers. However this presents a puzzle, since unraveling can only occur when firms are willing to make early offers and workers are willing to accept them. We present a model and experiment in which workers’ quality becomes known only in the late part of the market. However, in equilibrium, matching can occur (inefficiently) early only when there is comparable demand and supply: a surplus of applicants, but a shortage of high quality applicants.

The Effects of Entry in Bilateral Oligopoly

Author(s):Alex Dickson
Journal: Games
Publisher:
Abstract
| Pages: 283-303
The purpose of this paper is to study the effects of entry into the market for a single commodity in which both sellers and buyers are permitted to interact strategically. With the inclusion of an additional seller, the market is quasi-competitive: the price falls and volume of trade increases, as expected. However, contrary to the conventional wisdom, existing sellers’ payoffs may increase. The conditions under which entry by new sellers raises the equilibrium payoffs of existing sellers are derived. These depend in an intuitive way on the elasticity of a strategic analog of demand and the market share of existing sellers, and encompass entirely standard economic environments. Similar results are derived relating to the entry of additional buyers and the effects of entry on both sides of the market are investigated.

The Hitchhiker’s Guide to Adaptive Dynamics

Author(s):Åke Brännström -- Jacob Johansson -- Niels von Festenberg
Journal: Games
Publisher:
Abstract
| Pages: 304-328
Adaptive dynamics is a mathematical framework for studying evolution. It extends evolutionary game theory to account for more realistic ecological dynamics and it can incorporate both frequency- and density-dependent selection. This is a practical guide to adaptive dynamics that aims to illustrate how the methodology can be applied to the study of specific systems. The theory is presented in detail for a single, monomorphic, asexually reproducing population. We explain the necessary terminology to understand the basic arguments in models based on adaptive dynamics, including invasion fitness, the selection gradient, pairwise invasibility plots (PIP), evolutionarily singular strategies, and the canonical equation. The presentation is supported with a worked-out example of evolution of arrival times in migratory birds. We show how the adaptive dynamics methodology can be extended to study evolution in polymorphic populations using trait evolution plots (TEPs). We give an overview of literature that generalises adaptive dynamics techniques to other scenarios, such as sexual, diploid populations, and spatially-structured populations. We conclude by discussing how adaptive dynamics relates to evolutionary game theory and how adaptive-dynamics techniques can be used in speciation research.

Relative Concerns and Delays in Bargaining with Private Information

Author(s):Ana Mauleon -- Vincent Vannetelbosch
Journal: Games
Publisher:
Abstract
| Pages: 329-338
We consider Rubinstein’s two-person alternating-offer bargaining model with two-sided incomplete information. We investigate the effects of one party having relative concerns about the bargaining outcome and the delay in reaching an agreement. We find that facing an opponent with stronger relative concerns only hurts the bargainer when she is stronger than her opponent. In addition, we show that an increase of one party’s relative concerns will decrease the maximum delay in reaching an agreement.

Repeated Play of Families of Games by Resource-Constrained Players

Author(s):Arina Nikandrova
Journal: Games
Publisher:
Abstract
| Pages: 339-346
This paper studies a repeated play of a family of games by resource-constrained players. To economize on reasoning resources, the family of games is partitioned into subsets of games which players do not distinguish. An example is constructed to show that when games are played a finite number of times, partitioning of the game set according to a coarse exogenously given partition might introduce new symmetric equilibrium payoffs which Pareto dominate best equilibrium outcomes with distinguished games. Moreover, these new equilibrium payoffs are also immune to evolutionary pressure at the partition selection stage.

The Renegotiation-Proofness Principle and Costly Renegotiation

Author(s):James R. Brennan -- Joel Watson
Journal: Games
Publisher:
Abstract
| Pages: 347-366
We study contracting and costly renegotiation in settings of complete, but unverifiable information, using the mechanism-design approach. We show how renegotiation activity is best modeled in the fundamentals of the mechanism-design framework, so that noncontractibility of renegotiation amounts to a constraint on the problem. We formalize and clarify the Renegotiation-Proofness Principle (RPP), which states that any state-contingent payoff vector that is implementable in an environment with renegotiation can also be implemented by a mechanism in which renegotiation does not occur in equilibrium. We observe that the RPP is not valid in some settings. However, we prove a general monotonicity result that confirms the RPP’s message about renegotiation opportunities having negative consequences. Our monotonicity theorem states that, as the costs of renegotiation increase, the set of implementable state-contingent payoffs becomes larger.
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