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on Game Theory |
| By: | Christopher Kah; Markus Walzl |
| Abstract: | We propose a learning dynamic with agents using samples of past play to estimate the distribution of other players’ strategy choices and best responding to this estimate. To account for noisy play, estimated distributions over other players’ strategy choices have full support in the other players’ strategy sets for positive levels of noise and converge to the sampled distribution in the limit of vanishing noise. Recurrent classes of the dynamic process only contain admissible strategies and can be characterised by minimal CURB sets based on best responses to noisy play whenever the set of sampled distributions is sufficiently rich. In this case, the dynamic process will always end up in a set of strategies that contains the support of a (trembling hand) perfect equilibrium. If the perfect equilibrium is unique and in pure strategies, the equilibrium resembles the unique recurrent class of the dynamic process. We apply the dynamic process to learning in matching markets and sequential two player games with perfect information. |
| Keywords: | Best-response learning, equilibrium selection, stochastic stability, trembling hand perfection, CURB sets |
| JEL: | C72 C73 D83 |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:inn:wpaper:2015-15&r=gth |
| By: | Dan Kovenock (Economic Science Institute, Argyros School of Business and Economics, Chapman University); Brian Roberson (Purdue University, Department of Economics, Krannert School of Management) |
| Abstract: | Maintaining the security of critical infrastructure networks is vital for a modern economy. This paper examines a game-theoretic model of attack and defense of a network in which the defender's objective is to maintain network connectivity and the attacker's objective is to destroy a set of nodes that disconnects the network. The con ict at each node is modeled as a contest in which the player that allocates the higher level of force wins the node. Although there are multiple mixed-strategy equilibria, we characterize correlation structures in the players' multivariate joint distributions of force across nodes that arise in all equilibria. For example, in all equilibria the attacker utilizes a stochastic `guerrilla warfare' strategy in which a single random [minimal] set of nodes that disconnects the network is attacked. |
| Keywords: | Allocation Game, Asymmetric Con ict, Attack and Defense, Colonel Blotto Game, Network Connectivity, Weakest-Link, Best-Shot |
| JEL: | C7 D74 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:15-24&r=gth |
| By: | Stefan Rass |
| Abstract: | The game-theoretic risk management framework put forth in the precursor work "Towards a Theory of Games with Payoffs that are Probability-Distributions" (arXiv:1506.07368 [q-fin.EC]) is herein extended by algorithmic details on how to compute equilibria in games where the payoffs are probability distributions. Our approach is "data driven" in the sense that we assume empirical data (measurements, simulation, etc.) to be available that can be compiled into distribution models, which are suitable for efficient decisions about preferences, and setting up and solving games using these as payoffs. While preferences among distributions turn out to be quite simple if nonparametric methods (kernel density estimates) are used, computing Nash-equilibria in games using such models is discovered as inefficient (if not impossible). In fact, we give a counterexample in which fictitious play fails to converge for the (specifically unfortunate) choice of payoff distributions in the game, and introduce a suitable tail approximation of the payoff densities to tackle the issue. The overall procedure is essentially a modified version of fictitious play, and is herein described for standard and multicriteria games, to iteratively deliver an (approximate) Nash-equilibrium. |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1511.08591&r=gth |
| By: | Gerlagh, Reyer (Tilburg University, Center For Economic Research); van der Heijden, Eline (Tilburg University, Center For Economic Research) |
| Abstract: | We experimentally study decision-making in a novel dynamic coordination game. The game captures features of a transition between externality networks. Groups consisting of three subjects start in a stable benchmark equilibrium with network externality. Over seven rounds, they can transit to an alternative stable equilibrium based on the other network. The alternative network has higher payoffs, but the transition is slow and costly. Coordination is required to implement the transition while minimizing costs.<br/>In the experiment, the game is repeated five times, which enables groups to learn to coordinate over time. We compare a neutral language treatment with a ‘green framing’ treatment, in which meaningful context is added to the instructions. We find the green framing to significantly increase the number of profitable transitions, but also to inhibit the learning from past experiences, and thus it reduces coherence of strategies. Consequently, payoffs in both treatments are similar even though the green framing results in twice as many transitions.<br/>In the context of environmental policy, the experiment suggests general support for ‘going green’, but we also find evidence for anchoring of beliefs by green framing; proponents and opponents stick to their initial strategies. |
| Keywords: | cost of transition; lab experiment; dynamic stag hunt game; framing |
| JEL: | C73 C92 O44 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiucen:c3b6b46c-0fb0-4098-8251-d271d17b23e2&r=gth |
| By: | Arnaud Dragicevic (Chaire Forêts pour Demain, AgroParisTech-Office National des Forêts) |
| Abstract: | Economic agents have the possibility to fund the protection of environmental public goods, such as natural ecosystems and biodiversity, facing unknown risks of collapse, which could help to back them up. On the base of the prediction markets, which meet with a degree of success since their introduction, we propose an evolutionary model of an option fund market for the threshold environmental public goods. We consider population dynamics of agents distributed into proportional fair-share contributors and free-riders. The model outcomes show that the public goods could be provided when the agents exchanging option contracts are equally divided into buyers and sellers. This result only holds for a specific social belief over the probability of the public good safeguard, the strict equality between bids and asks, and the equality of all payoffs. Otherwise, providing public goods through option markets turns out to be inoperative. |
| Keywords: | bioeconomics; evolutionary game theory; random-matching; uncertainty; prediction markets; conservation banking. |
| JEL: | C73 D81 H41 Q57 |
| Date: | 2015–12 |
| URL: | http://d.repec.org/n?u=RePEc:lef:wpaper:2015-12&r=gth |
| By: | Oswaldo Gressani (CREA, Université de Luxembourg) |
| Abstract: | We develop an equilibrium concept coined Endogeneous Quantal Response Equilibrium (EQRE) based on heterogeneous players and endogeneous learning in a logistic quantal choice model. Each player has an asymptotically consistent estimate of his rival's rationality index and is able to choose his own rationality level according to a cost-benefit tradeoff This approach allows to enrich bounded rationality models by incorporating heterogeneous skills and by bridging the gap between stylized facts on the rationality index dynamics and a learning dimension. |
| Keywords: | Quantal Response Equilibrium, bounded rationality, learning |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:luc:wpaper:15-18&r=gth |
| By: | Jean-Paul Carvalho (Department of Economics, University of California-Irvine) |
| Abstract: | In club models of religion, sacrifices demanded by religious groups promote efficient production of club goods by screening out free riders. An alternative, complementary view is that religious clubs provide a means of sorting, matching individuals with similar characteristics. Sorting differs from screening in that it operates on traits that do not directly affect club goods production. This paper explores the role of sacrifice in sorting among religious clubs when individuals prefer to interact with their own type. Despite this own-type bias, the usual free- rider problem in club goods production can inhibit sorting among groups. Pro- hibitions and demands for stigmatizing behavior can solve this problem. Costly sacrifices are demanded, not by groups catering to the majority, but by those attracting rare/exotic types. The rarer the type, the more costly the sacrifice required to a chieve sorting. |
| Keywords: | Club goods,;Economics of religion; Sorting |
| JEL: | C72 C73 Z1 |
| Date: | 2015–10 |
| URL: | http://d.repec.org/n?u=RePEc:irv:wpaper:151604&r=gth |
| By: | F.Javier Martínez-de-Albéniz (Universitat de Barcelona); Carles Rafels (Universitat de Barcelona); Neus Ybern (Universitat Politècnica de Catalunya) |
| Abstract: | We show that the family of assignment matrices which give rise to the same nucleolus form a compact join-semilattice with one maximal element, which is always a valuation (see p.43, Topkis (1998)). We give an explicit form of this valuation matrix. The above family is in general not a convex set, but path-connected, and we construct minimal elements of this family. We also analyze the conditions to ensure that a given vector is the nucleolus of some assignment game. |
| Keywords: | Assignment game, core, nucleolus, semilattice. |
| JEL: | C71 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:ewp:wpaper:333web&r=gth |
| By: | Briana Chang (School of Business, University of Wisconsin–Madison;); Shengxing Zhang (Department of Economics, London School of Economics (LSE); Centre for Macroeconomics (CFM)) |
| Abstract: | This paper proposes a theory of intermediation in which intermediaries emerge endogenously as the choice of agents. In contrast to the previous trading models based on random matching or exogenous networks, we allow traders to explicitly choose their trading partners as well as the number of trading links in a dynamic framework. We show that traders with higher trading needs optimally choose to match with traders with lower needs for trade and they build fewer links in equilibrium. As a result, traders with the least trading need turn out to be the most connected and have the highest gross trade volume. The model therefore endogenously generates a core-periphery trading network that we often observe: a financial architecture that involves a small number of large, interconnected institutions. We use this framework to study bid-ask spreads, trading volume, asset allocation and implications on systemic risk. |
| Keywords: | Over-the-Counter Market, Trading Network, Matching, Intermediation |
| JEL: | C70 G1 G20 |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:cfm:wpaper:1534&r=gth |
| By: | HIRATA, Daisuke; KASUYA, Yusuke |
| Abstract: | This paper studies stable and (one-sided) strategy-proof matching rules in many-to-one matching markets with contracts. First, the number of such rules is shown to be at most one. Second, the doctor-optimal stable rule, whenever it exists, is shown to be the unique candidate for a stable and strategy-proof rule. Third, a stable and strategy-proof rule, when exists, is shown to be second-best optimal for doctor welfare, in the sense that no individually-rational and strategy-proof rule can dominate it. This last result is further generalized to non-wasteful and strategy-proof rules. Notably, all those results are established without any substitutes conditions on hospitals' choice functions, and hence, the proofs do not rely on the "rural hospital" theorem. We also show by example that the outcomes of a stable and strategy-proof rule do not always coincide with those of the cumulative offer process; hence, the above results hold NOT because the cumulative offer process is the only candidate for stable and strategy-proof rules. |
| Keywords: | matching with contracts, stability, strategy-proofness, uniqueness, efficiency, irrelevance of rejected contracts |
| Date: | 2015–09–25 |
| URL: | http://d.repec.org/n?u=RePEc:hit:econdp:2015-10&r=gth |
| By: | Hart, Sergiu (Department of Economics, Institute of Mathematics, and Federmann Center for the Study of Rationality, The Hebrew University of Jerusalem.); Kremer, Ilan (Department of Economics, Business School, and Federmann Center for the Study of Rationality, The Hebrew University of Jerusalem; Department of Economics, University of Warwick); Perry, Motty (Federmann Center for the Study of Rationality, The Hebrew University of Jerusalem; Department of Economics, University of Warwick.) |
| Abstract: | An evidence game is a strategic disclosure game in which an informed agent who has some pieces of verifiable evidence decides which ones to disclose to an uninformed principal who chooses a reward. The agent, regardless of his information, prefers the reward to be as high as possible. We compare the setup where the principal chooses the reward after the evidence is disclosed to the mechanism-design setup where he can commit in advance to a reward policy. The main result is that under natural conditions on the truth structure of the evidence, the two setups yield the same equilibrium outcome. |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:wcreta:06&r=gth |
| By: | Rodrigo A. Velez (Texas A&M University, Department of Economics) |
| Abstract: | We characterize the family of non-contestable budget- monotone rules for the allocation of objects and money as those obtained by maximizing a min social welfare function among all non-contestable allocations. We provide three additional seemingly independent approaches to construct these rules. We present three applications of this characterization. First, we show that one can "rectify" any non-contestable rule without losing non-contestability. Second, we characterize the preferences that admit, for each budget, a non-contestable allocation satisfying a minimal or maximal individual consumption of money constraint. Third, we study continuity properties of the non-contestable correspondence. |
| Keywords: | solidarity, allocationof objects andmoney, non contestable allocations |
| JEL: | D61 D63 D70 |
| Date: | 2015–12–01 |
| URL: | http://d.repec.org/n?u=RePEc:txm:wpaper:20151201-001&r=gth |
| By: | Anderson, Edward (University of Sydney); Holmberg, Pär (Research Institute of Industrial Economics (IFN)) |
| Abstract: | We consider a procurement auction, where each supplier has private costs and submits a stepped supply function. We solve for a Bayesian Nash equilibrium and show that the equilibrium has a price instability in the sense that a minor change in a supplier.s cost sometimes result in a major change in the market price. In wholesale electricity markets, we predict that the bid price of the most expensive production unit can change by 1-10% due to price instability. The price instability is reduced when suppliers have more steps in their supply functions for a given production technology. In the limit, as the number of steps increases and the cost uncertainty decreases, the Bayesian equilibrium converges to a pure-strategy NE without price instability, the Supply Function Equilibrium (SFE). |
| Keywords: | Multi-unit auctions; indivisible unit; price instability; Bayesian Nash equilibria; supply function equilibria; convergence of Nash equilibria; whole-sale electricity markets |
| JEL: | C62 C72 D43 D44 L94 |
| Date: | 2015–11–27 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:iuiwop:1095&r=gth |
| By: | Dutta, Bhaskar (University of Warwick); Vohra, Rajiv (Brown University) |
| Abstract: | In the study of farsighted coalitional behavior, a central role is played by the von Neumann-Morgenstern (1944) stable set and its modification that incorporates farsightedness. Such a modification was first proposed by Harsanyi (1974) and has recently been re-formulated by Ray and Vohra (2015). The farsighted stable set is based on a notion of indirect dominance in which an outcome can be dominated by a chain of coalitional ‘moves’ in which each coalition that is involved in the sequence eventually stands to gain. However, it does not require that each coalition make a maximal move, i.e., one that is not Pareto dominated (for the members of the coalition in question) by another. Nor does it restrict coalitions to hold common expectations regarding the continuation path from every state. Consequently, when there are multiple continuation paths the farsighted stable set can yield unreasonable predictions. We resolve this difficulty by requiring all coalitions to have common rational expectations about the transition from one outcome to another. This leads to two related concepts: the rational expectations farsighted stable set (REFS) and the strong rational expectations farsighted stable set (SREFS). We apply these concepts to simple games and to pillage games to illustrate the consequences of imposing rational expectations for farsighted stability. |
| Keywords: | stable sets ; farsightedness ; consistency ; maximality ; rational expectations ; simple games ; pillage games. JEL Classification Numbers: C71 ; D72 ; D74 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:wcreta:05&r=gth |
| By: | Nicolas Sahuguet; Paola Conconi; Maurizio Zanardi |
| Keywords: | interstate conflicts; democratic peace; elections; term limits |
| JEL: | C72 D72 F00 |
| Date: | 2015–10 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/217949&r=gth |
| By: | Harry Clarke (University of Melbourne) |
| Abstract: | The economics of global climate mitigation is discussed when there is imperfect knowledge of future climatic changes, of policy effectiveness and of the policy responses by different countries. Uncertainty is accounted for by using heuristics derived from classical decision rules. These heuristics provide plausible policy rules that depend on only limited information. They emphasize the possibility of “getting it wrong” in terms of the appropriate scale of policy response and from policy failure itself. The minimax rule or Precautionary Principle, which targets “worst case” situations, is not useful unless policies are effective with certainty. However the widespread presumption that policy action is warranted if climate-induced losses without action are “large" relative to costs of policy can be justified using minimax regret reasoning. The global analysis is extended to individual national decision-making when nations jointly play a game against nature with policy spillovers. Simultaneous moves game solutions as well as heuristics are provided and indicate how policy actions are best determined for individual countries rather than for a global authority. |
| Keywords: | climate risks and uncertainties; mitigation policy |
| JEL: | D84 Q54 C70 |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:een:ccepwp:1512&r=gth |
| By: | Anton Bondarev; Phemelo Tamasiga (University of Basel) |
| Abstract: | The paper presents a model of world economy with two countries where one of them dubbed home sells the exhaustible resource to final producers in both countries, which compete at the final goods market. The interaction between final producers is reached via the sticky price mechanics, whereas price continuously adjusts to produced final product quantities. Production technology in both countries includes the resource as an essential input plus the variety of intermediate products. We demonstrate how opening up to trade of the exhaustible resource may be beneficial for the home economy by promoting technical change and capital accumulation via increased resource rents and relative factor prices movements. This leads to the increase in social welfare due to taste for variety and fosters structural change in the home country. |
| Keywords: | structural change, resource economics, international trade, differential games |
| JEL: | F1 L16 Q37 C6 C7 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:bsl:wpaper:2014/14&r=gth |
| By: | Haluk Ergin (University of California, Berkeley); Tayfun Sönmez (Boston College); M. Utku Ünver (Boston College) |
| Abstract: | Owing to the worldwide shortage of deceased donor organs for transplantation, tissue/organ donations from living donors have become a signicant source for transplantation for various organs including kidneys, livers, and lungs. However, not all willing living donors can donate to their intended patients because of medical incompatibility between donor and patient. Such incompatibilities can be overcome by an exchange (of donors) between patients with incompatible donors. Such exchanges have become widespread in the last decade for kidneys with the introduction of optimization and market design techniques to kidney exchange. Following the success of kidney exchange, a small but growing number of liver exchanges has also been conducted. However, even though living-donor lung transplantation was introduced more than two decades ago, lung exchange is neither practiced nor introduced. From an organizational perspective, living donation is more involved for lungs than kidneys or livers because it often requires two donors. While this makes living donation more dicult for lungs, it also means that the role of exchange might be more prominent for living-donor lung transplantation. We introduce lung exchange as a novel transplantation modality, develop an analytical lung-exchange model, and introduce optimal lung-exchange mechanisms under various logistical constraints. Our simulations suggest that the number of living-donor lung transplants can be doubled by allowing 2-way and 3-way exchanges alone, and can be tripled in the absence of logistical constraints. |
| Keywords: | Market Design, Matching, Complementarities, Lung Exchange, Organ Exchange |
| JEL: | C78 |
| Date: | 2015–11–23 |
| URL: | http://d.repec.org/n?u=RePEc:boc:bocoec:886&r=gth |