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An Equilibrium Analysis of Knaster’s Fair Division Procedure

Author(s):Matt Van Essen
Journal: Games
Publisher:
Abstract
| Pages: 21-37
In an incomplete information setting, we analyze the sealed bid auction proposed by Knaster (cf. Steinhaus (1948)). This procedure was designed to efficiently and fairly allocate multiple indivisible items when participants report their valuations truthfully. In equilibrium, players do not follow truthful bidding strategies. We find that, ex-post, the equilibrium allocation is still efficient but may not be fair. However, on average, participants receive the same outcome they would have received if everyone had reported truthfully—i.e., the mechanism is ex-ante fair.

Nash Implementation in an Allocation Problem with Single-Dipped Preferences

Author(s):Ahmed Doghmi
Journal: Games
Publisher:
Abstract
| Pages: 38-49
In this paper, we study the Nash implementation in an allocation problem with single-dipped preferences. We show that, with at least three agents, Maskin monotonicity is necessary and sufficient for implementation. We examine the implementability of various social choice correspondences (SCCs) in this environment, and prove that some well-known SCCs are Maskin monotonic ( but they do not satisfy no-veto power) and hence Nash implementable.

Tacit Collusion under Fairness and Reciprocity

Author(s):Doruk İriş -- Luís Santos-Pinto
Journal: Games
Publisher:
Abstract
| Pages: 50-65
This paper departs from the standard profit-maximizing model of firm behavior by assuming that firms are motivated in part by personal animosity–or respect–towards their competitors. A reciprocal firm responds to unkind behavior of rivals with unkind actions (negative reciprocity), while at the same time, it responds to kind behavior of rivals with kind actions (positive reciprocity). We find that collusion is easier to sustain when firms have a concern for reciprocity towards competing firms provided that they consider collusive prices to be kind and punishment prices to be unkind. Thus, reciprocity concerns among firms can have adverse welfare consequences for consumers.

Hierarchical Bayesian Analysis of Biased Beliefs and Distributional Other-Regarding Preferences

Author(s):Ozan Aksoy -- Jeroen Weesie
Journal: Games
Publisher:
Abstract
| Pages: 66-88
This study investigates the relationship between an actor’s beliefs about others’ other-regarding (social) preferences and her own other-regarding preferences, using an “avant-garde” hierarchical Bayesian method. We estimate two distributional other-regarding preference parameters, α and β, of actors using incentivized choice data in binary Dictator Games. Simultaneously, we estimate the distribution of actors’ beliefs about others α and β, conditional on actors’ own α and β, with incentivized belief elicitation. We demonstrate the benefits of the Bayesian method compared to it’s hierarchical frequentist counterparts. Results show a positive association between an actor’s own (α; β ) and her beliefs about average(α; β) in the population. The association between own preferences and the variance in beliefs about others’ preferences in the population, however, is curvilinear for α and insignificant for β. These results are partially consistent with the cone effect [1,2] which is described in detail below. Because in the Bayesian-Nash equilibrium concept, beliefs and own preferences are assumed to be independent, these results cast doubt on the application of the Bayesian-Nash equilibrium concept to experimental data.

Group Size, Coordination, and the Effectiveness of Punishment in the Voluntary Contributions Mechanism: An Experimental Investigation

Author(s):Bin Xu -- C. Bram Cadsby -- Liangcong Fan -- Fei Song
Journal: Games
Publisher:
Abstract
| Pages: 89-105
We examine the effectiveness of the individual-punishment mechanism in larger groups, comparing groups of four to groups of 40 participants. We find that the individual punishment mechanism is remarkably robust when the marginal per capita return (MPCR), i.e. the return to each participant from each dollar that is contributed, is held constant. Moreover, the efficiency gains from the punishment mechanism are significantly higher in the 40-participant than in the four-participant treatment. This is true despite the coordination problems inherent in an institution relying on decentralized individual punishment decisions in the context of a larger group. It reflects increased per capita expenditures on punishment that offset the greater coordination difficulties in the larger group. However, if the marginal group return (MGR), i.e. the return to the entire group of participants, stays constant, resulting in an MPCR that shrinks with group size, no such offset occurs and punishment loses much but not all of its effectiveness at encouraging voluntary contributions to a public good. Efficiency is not significantly different from the small-group treatment.

Divorce Costs and Marital Dissolution in a One-to-One Matching Framework With Nontransferable Utilities

Author(s):Ismail Saglam
Journal: Games
Publisher:
Abstract
| Pages: 106-124
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.

Two Pricing Mechanisms in Sponsored Search Advertising

Author(s):Wei Yang -- Youyi Feng -- Baichun Xiao
Journal: Games
Publisher:
Abstract
| Pages: 125-143
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.

Reciprocity in Locating Contributions: Experiments on the Neighborhood Public Good Game

Author(s):Siegfried Berninghaus -- Werner Güth -- Stephan Schosser
Journal: Games
Publisher:
Abstract
| Pages: 144-162
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.

The Dynamics of Costly Signaling

Author(s):Elliott O. Wagner
Journal: Games
Publisher:
Abstract
| Pages: 163-181
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.
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