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on Game Theory |
| By: | Herings, P.J.J. (Tilburg University); Laan, G. van der; Talman, A.J.J. (Tilburg University); Yang, Z.F. (Tilburg University) |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:ner:tilbur:urn:nbn:nl:ui:12-3736837&r=gth |
| By: | Itai Arieli |
| Abstract: | In 1995, Aumann showed that in games of perfect information, common knowledge of rationality is consistent and entails the back- ward induction (BI) outcome. That work has been criticized because it uses "counterfactual" reasoning|what a player "would" do if he reached a node that he knows he will not reach, indeed that he him- self has excluded by one of his own previous moves. This paper derives an epistemological characterization of BI that is outwardly reminiscent of Aumann's, but avoids counterfactual reason- ing. Specifically, we say that a player strongly believes a proposition at a node of the game tree if he believes the proposition unless it is logically inconsistent with that node having been reached. We then show that common strong belief of rationality is consistent and entails the BI outcome, where - as with knowledge - the word "common" signifies strong belief, strong belief of strong belief, and so on ad infinitum. Our result is related to - though not easily derivable from - one obtained by Battigalli and Sinischalchi [7]. Their proof is, however, much deeper; it uses a full-blown semantic model of probabilities, and belief is defined as attribution of probability 1. However, we work with a syntactic model, defining belief directly by a sound and complete set of axioms, and the proof is relatively direct. |
| Date: | 2010–02 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp535&r=gth |
| By: | Niels D. Grosse (School of Economics and Business Administration, Friedrich-Schiller-University Jena) |
| Abstract: | This paper investigates the effects of neighborhood size and network structure on strategic experimentation. We analyze a multi-arm bandit game with one safe and two risky alternatives. In this setting, risk taking produces a learning externality and an opportunity for free riding. We conduct a laboratory experiment to investigate whether group size and the network structure affect risk taking. We find that group size has an effect on risk taking that is qualitatively in line with equilibrium predictions. Introducing an asymmetry among agents in the same network with respect to neighborhood size leads to substantial deviations from equilibrium play. Findings suggests that subjects react to changes in their direct neighborhood but fail to play a best-response to their position within the network. |
| Keywords: | strategic experimentation, experiment, bandit game, risk taking |
| JEL: | C91 D81 D85 O33 |
| Date: | 2010–02–23 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2010-011&r=gth |
| By: | Edith Cohen; Michal Feldman; Amos Fiat; Haim Kaplan; Svetlana Olonetsky |
| Abstract: | We study auctions with additive valuations where agents have a limit on the number of items they may receive. We refer to this setting as capacitated allocation games. We seek truthful and envy free mechanisms that maximize the social welfare. I.e., where agents have no incentive to lie and no agent seeks to exchange outcomes with another. In 1983, Leonard showed that VCG with Clarke Pivot payments (which is known to be truthful, individually rational, and have no positive transfers), is also an envy free mechanism for the special case of n items and n unit capacity agents. We elaborate upon this problem and show that VCG with Clarke Pivot payments is envy free if agent capacities are all equal. When agent capacities are not identical, we show that there is no truthful and envy free mechanism that maximizes social welfare if one disallows positive transfers. For the case of two agents (and arbitrary capacities) we show a VCG mechanism that is truthful, envy free, and individually rational, but has positive transfers. We conclude with a host of open problems that arise from our work. |
| Date: | 2010–02 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp540&r=gth |
| By: | Noga Alon; Yuval Emek; Michal Feldman; Moshe Tennenholtz |
| Abstract: | We quantify the effect of Bayesian ignorance by comparing the social cost obtained in a Bayesian game by agents with local views to the expected social cost of agents having global views. Both benevolent agents, whose goal is to minimize the social cost, and selfish agents, aiming at minimizing their own individual costs, are considered. When dealing with selfish agents, we consider both best and worst equilibria outcomes. While our model is general, most of our results concern the setting of network cost sharing (NCS) games. We provide tight asymptotic results on the effect of Bayesian ignorance in directed and undirected NCS games with benevolent and selfish agents. Among our findings we expose the counter-intuitive phenomenon that “ignorance is blissâ€: Bayesian ignorance may substantially improve the social cost of selfish agents. We also prove that public random bits can replace the knowledge of the common prior in attempt to bound the effect of Bayesian ignorance in settings with benevolent agents. Together, our work initiates the study of the effects of local vs. global views on the social cost of agents in Bayesian contexts. |
| Keywords: | Bayesian games; local vs. global view; network cost sharing; |
| Date: | 2010–02 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp538&r=gth |
| By: | Noga Alon; Michal Feldman; Ariel D. Procaccia; Moshe Tennenholtz |
| Abstract: | We consider the problem of locating a facility on a network, represented by a graph. A set of strategic agents have different ideal locations for the facility; the cost of an agent is the distance between its ideal location and the facility. A mechanism maps the locations reported by the agents to the location of the facility. Specifically, we are interested in social choice mechanisms that do not utilize payments. We wish to design mechanisms that are strategyproof, in the sense that agents can never benefit by lying, or, even better, group strategyproof, in the sense that a coalition of agents cannot all benefit by lying. At the same time, our mechanisms must provide a small approximation ratio with respect to one of two optimization targets: the social cost or the maximum cost. We give an almost complete characterization of the feasible truthful approximation ratio under both target functions, deterministic and randomized mechanisms, and with respect to different network topologies. Our main results are: We show that a simple randomized mechanism is group strategyproof and gives a tight approximation ratio of 3/2 for the maximum cost when the network is a circle; and we show that no randomized SP mechanism can provide an approximation ratio better than 2-o(1) to the maximum cost even when the network is a tree, thereby matching a trivial upper bound of two. |
| Date: | 2010–02 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp541&r=gth |
| By: | Robert J. Aumann |
| Abstract: | A response to criticism of the paper "On the Matter of the Man with Three Wives," Moriah 22 (1999), 98- 107 (see also Rationality Center DP 102, June 1996). The Moriah paper is a non- mathematical account, written in Hebrew for the Rabbinic public, of "Game- Theoretic Analysis of a Bankruptcy Problem from the Talmud," by R. Aumann and M. Maschler, J. Econ. Th. 36 (1985), 195- 213. The current response appeared in Hama'yan 50 (2010), 1- 11. |
| Date: | 2010–02 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp537&r=gth |
| By: | David Gill; John Thanassoulis |
| Abstract: | In many markets firms set posted prices which are potentially negotiable. We analyze the optimal marketing mix of pricing and bargaining when price takers buy at posted prices but bargainers attempt to negotiate discounts. The optimal bargaining strategy involves the firms offering bargainers randomly-sized discounts. Competing firms keep posted prices high to weaken the bargainers’ outside option, thus forgoing the chance to increase profits from price takers by undercutting their rival. A range of posted price equilibria are possible, and the higher price in the range inrceases when the proportion of bargainers goes up or the bargainers become less skilled. We consider how firms and competition authorities might encourage more consumers to bargain and determine the conditions under which each would choose to do so. Finally, we study the firms’ strategic decision about how much bargaining discretion sales staff should be allowed. Both firms allowing full bargaining flexibility is always an equilibrium - but not always the most profitable one. If there are enough bargainers, both firms committing to only matching the rival’s posted price is also an equilibrium: price matching moderates competition, thus raising profits. |
| Keywords: | Posted prices, List prices, Bargaining, Negotiation, Haggling, Discounts, Outside option, Price takers, Competition policy, Price matching |
| JEL: | C78 D43 L13 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:479&r=gth |
| By: | Gregory Pavlov (University of Western Ontario) |
| Abstract: | We extend the ‘no-haggling’ result of Riley and Zeckhauser (1983) to the class of linear multiproduct monopoly problems when the buyer’s valuations are smoothly distributed. In particular we show that there is no loss for the seller in optimizing over mechanisms such that all allocations belong to the boundary of the feasible set. The set of potentially optimal mechanisms can be further restricted when the costs are sufficiently low: the optimal mechanisms use only allocations from the ‘north-east’ boundary of the feasible set and the null allocation. |
| Keywords: | Multidimensional screening; Price discrimination; Optimal selling strategies; Mechanism design |
| JEL: | C78 D42 D82 L11 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:uwo:uwowop:20102&r=gth |
| By: | Gregory Pavlov (University of Western Ontario) |
| Abstract: | We solve for the optimal mechanism for selling two goods when the buyer’s demand characteristics are unobservable. In the case of substitutable goods, the seller has an incentive to offer lotteries over goods in order to charge the buyers with large differences in the valuations a higher price for obtaining their desired good with certainty. However, the seller also has a countervailing incentive to make the allocation of the goods among the participating buyers more efficient in order to increase the overall demand. In the case when the buyer can consume both goods, the seller has an incentive to underprovide one of the goods in order to charge the buyers with large valuations a higher price for the bundle of both goods. As in the case of substitutable goods, the seller also has a countervailing incentive to lower the price of the bundle in order to increase the overall demand. |
| Keywords: | Multidimensional screening; Price discrimination; Optimal selling strategies; Mechanism design |
| JEL: | C78 D42 D82 L11 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:uwo:uwowop:20103&r=gth |
| By: | Siddhartha Bandyopadhyay; Kalan Chatterjee |
| Abstract: | We consider the effect of giving incentives to ordinary citizens to report po- tential criminal activity. Additionally we look at the effect of "pro ling" and biased reporting. If police single out or pro le a group for more investiga- tion, then crime in the pro led group decreases. If a certain group is reported on more frequently through biased reporting by citizens, crime in the group reported on actually increases. In the second model, we consider a neigh- bourhood structure where individuals get information on possible criminal activity by neighbours on one side and decide whether to report or not based on the signal. When costs of reporting are low relative to the cost of being investigated, costs of investigation are increasing in the number of reports and there is at least one biased individual, we show there is a "contagion equilibrium" where everyone reports his or her neighbour. |
| Keywords: | Neighbourhood, crime reporting and profiling |
| JEL: | C72 D82 |
| Date: | 2010–02 |
| URL: | http://d.repec.org/n?u=RePEc:bir:birmec:06-04r&r=gth |