|
on Game Theory |
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Issue of 2012‒10‒20
sixteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Committee, Nobel Prize (Nobel Prize Committee) |
| Abstract: | Economists study how societies allocate resources. Some allocation problems are solved by the price system: high wages attract workers into a particular occupation, and high energy prices induce consumers to conserve energy. In many instances, however, using the price system would encounter legal and ethical objections. Consider, for instance, the allocation of public-school places to children, or the allocation of human organs to patients who need transplants. Furthermore, there are many markets where the price system operates but the traditional assumption of perfect competition is not even approximately satisfied. In particular, many goods are indivisible and heterogeneous, whereby the market for each type of good becomes very thin. How these thin markets allocate resources depends on the institutions that govern transactions. |
| Keywords: | Market Design; |
| JEL: | C71 D02 |
| Date: | 2012–10–15 |
| URL: | http://d.repec.org/n?u=RePEc:ris:nobelp:2012_001&r=gth |
| By: | Committee, Nobel Prize (Nobel Prize Committee) |
| Abstract: | This year’s Prize to Lloyd Shapley and Alvin Roth extends from abstract theory developed in the 1960s, over empirical work in the 1980s, to ongoing efforts to find practical solutions to real-world problems. Examples include the assignment of new doctors to hospitals, students to schools, and human organs for transplant to recipients. Lloyd Shapley made the early theoretical contributions, which were unexpectedly adopted two decades later when Alvin Roth investigated the market for U.S. doctors. His findings generated further analytical developments, as well as practical design of market institutions. |
| Keywords: | Market Design; |
| JEL: | C71 D02 |
| Date: | 2012–10–15 |
| URL: | http://d.repec.org/n?u=RePEc:ris:nobelp:2012_002&r=gth |
| By: | Ori Haimanko (BGU); Atsushi Kajii (KIER, Kyoto University) |
| Abstract: | We relax the Kajii and Morris (1997a) notion of equilibrium ro- bustness by allowing approximate equilibria in close incomplete infor- mation games. The new notion is termed "approximate robustness". The approximately robust equilibrium correspondence turns out to be upper hemicontinuous, unlike the (exactly) robust equilibrium corre- spondence. As a corollary of the upper hemicontinuity, it is shown that approximately robust equilibria exist in all two-player zero-sum games and all two-player two-strategy games, whereas (exactly) robust equilibria may fail to exist for some games in these categories. |
| Keywords: | incomplete information, robustness, Bayesian Nash equi- librium, ?-equilibrium, upper hemicontinuity, zero-sum games. |
| JEL: | C72 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:bgu:wpaper:1209&r=gth |
| By: | Fabrizio, Germano; Peio, Zuazo Garín |
| Abstract: | We extend Aumann's [3] theorem deriving correlated equilibria as a consequence of common priors and common knowledge of rationality by explicitly allowing for non-rational behavior. We replace the assumption of common knowledge of rationality with a substantially weaker notion, joint p-belief of rationality, where agents believe the other agents are rational with probabilities p = (pi)i2I or more. We show that behavior in this case constitutes a constrained correlated equilibrium of a doubled game satisfying certain p-belief constraints and characterize the topological structure of the resulting set of p-rational outcomes. We establish continuity in the parameters p and show that, for p su ciently close to one, the p-rational outcomes are close to the correlated equilibria and, with high probability, supported on strategies that survive the iterated elimination of strictly dominated strategies. Finally, we extend Aumann and Dreze's [4] theorem on rational expectations of interim types to the broader p-rational belief systems, and also discuss the case of non-common priors. |
| Keywords: | bounded rationality, correlated equilibrium, aproximate common knowledge, p-rational blief system, common prior, information noncooperative game |
| Date: | 2012–07–16 |
| URL: | http://d.repec.org/n?u=RePEc:ehu:ikerla:8757&r=gth |
| By: | José Alvaro Rodrigues-Neto |
| Abstract: | A partitional model of knowledge is monotonic if there exists a linear order on the state space such that, for every player, each element of her partition contains only a sequence of consecutive states. In monotonic models, the absence of alternating cycles is equivalent to the property that, for every pair of players, the join of their partitions contains only singletons. Under these equivalent conditions any set of posterior beliefs for the players is consistent (i.e., there is a common prior). We describe the lattice properties of monotonic models, develop a test to check if a model is monotonic, propose a simple sufficient condition for non-monotonicity, and provide some examples. We also study models having circular orders, a weakening of monotonicity. |
| JEL: | C02 D80 D82 D83 |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:acb:cbeeco:2012-586&r=gth |
| By: | Aureo de Paula (Institute for Fiscal Studies and University of Pennsylvania) |
| Abstract: | This article reviews the recent literature on the econometric analysis of games where multiple solutions are possible. Multiplicity does not necessarily preclude the estimation of a particular model (and in certain cases even improves its identification), but ignoring it can lead to misspecifications. The survey starts with a general characterisation of structural models that highlights how multiplicity affects the classical paradigm. Because the information structure is an important guide to identification and estimation strategies, I discuss games of complete and incomplete information separately. Whereas many of the techniques discussed in the article can be transported across different information environments, some of them are specific to particular models. I also survey models of social interactions in a different section. I close with a brief discussion of post-estimation issues and research prospects. |
| Keywords: | Identification, multiplicity, games, social interactions |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:29/12&r=gth |
| By: | J. Atsu Amegashie (Department of Economics, University of Guelph.) |
| Abstract: | I present a two-player nested contest which is a convex combination of two widely studied contests: the Tullock (lottery) contest and the all-pay auction. A Nash equilibrium exists for all parameters of the nested contest. If and only if the contest is sufficiently asymmetric, then there is an equilibrium in pure strategies. In this equilibrium, individual and aggregate efforts are lower relative to the efforts in a Tullock contest. This leads to the surprising result that if aggregate efforts in the all-pay auction are higher than the aggregate efforts in the Tullock contest, then aggregate efforts in the nested contest may not lie between aggregate efforts in the all-pay auction and aggregate efforts in the Tullock contest. When the contest is symmetric or asymmetric, I find a mixed-strategy equilibrium and describe some properties of the equilibrium distribution function; I also find the equilibrium payoffs and expected bids. When the weight on the all-pay auction component of this nested contest lies in an intermediate range, then there exist multiple non-payoff-equivalent equilibria such that there is an all-pay auction equilibrium as defined in Alcade and Dahm (2010) and another equilibrium which is not an all-pay auction equilibrium; these equilibria cannot be ranked using the Pareto criterion. If the goal of a contest-designer is to reduce aggregate effort (i.e., wasteful rent-seeking efforts), then this nested contest may be better than both the Tullock contest and the all-pay auction. |
| Keywords: | all-pay auction, discontinuous games, mixed strategy, pure strategy, Tullock contest. |
| JEL: | D72 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:gue:guelph:2012-11&r=gth |
| By: | Imre Kondor; Istv\'an Csabai; G\'abor Papp; Enys Mones; G\'abor Czimbalmos; M\'at\'e Csaba S\'andor |
| Abstract: | Correlations and other collective phenomena in a schematic model of heterogeneous binary agents (individual spin-glass samples) are considered on the complete graph and also on 2d and 3d regular lattices. The system's stochastic dynamics is studied by numerical simulations. The dynamics is so slow that one can meaningfully speak of quasi-equilibrium states. Performing measurements of correlations in such a quasi-equilibrium state we find that they are random both as to their sign and absolute value, but on average they fall off very slowly with distance in all instances that we have studied. This means that the system is essentially non-local, small changes at one end may have a strong impact at the other. Correlations and other local quantities are extremely sensitive to the boundary conditions all across the system, although this sensitivity disappears upon averaging over the samples or partially averaging over the agents. The strong, random correlations tend to organize a large fraction of the agents into strongly correlated clusters that act together. If we think about this model as a distant metaphor of economic agents or bank networks, the systemic risk implications of this tendency are clear: any impact on even a single strongly correlated agent will spread, in an unforeseeable manner, to the whole system via the strong random correlations. |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1210.3324&r=gth |
| By: | Erte Xiao; Howard Kunreuther |
| Abstract: | Previous findings on punishment have focused on environments in which the outcomes are known with certainty. In this paper, we conduct experiments to investigate how punishment affects cooperation in a two-person stochastic prisoner’s dilemma environment where each person can decide whether or not to cooperate, and the outcomes of alternative strategies are specified probabilistically under a transparent information condition. In particular, we study two types of punishment mechanisms: 1) an unrestricted punishment mechanism: both persons can punish; and 2) a restricted punishment mechanism: only cooperators can punish non-cooperators. We show that the restricted punishment mechanism is more effective in promoting cooperative behavior than the unrestricted one in a deterministic social dilemma. More importantly, the restricted type is less effective in an environment where the outcomes are stochastic than when they are known with certainty. Our data suggest that one explanation is that non-cooperative behavior is less likely to be punished when there is outcome uncertainty. Our findings provide useful information for designing efficient incentive mechanisms to induce cooperation in a stochastic social dilemma environment. |
| JEL: | C72 C73 C91 D02 D03 |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:18458&r=gth |
| By: | Jeffrey Butler; Paola Giuliano; Luigi Guiso |
| Abstract: | Trust beliefs are heterogeneous across individuals and, at the same time, persistent across generations. We investigate one mechanism yielding these dual patterns: false consensus. In the context of a trust game experiment, we show that individuals extrapolate from their own type when forming trust beliefs about the same pool of potential partners - i.e., more (less) trustworthy individuals form more optimistic (pessimistic) trust beliefs - and that this tendency continues to color trust beliefs after several rounds of game-play. Moreover, we show that ones own type/trustworthiness can be traced back to the values parents transmit to their children during their upbringing. In a second closely-related experiment, we show the economic impact of mis-calibrated trust beliefs stemming from false consensus. Miscalibrated beliefs lower participants experimental trust game earnings by about 20 percent on average. |
| JEL: | A1 A12 D01 Z1 |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:18460&r=gth |
| By: | Irma Clots-Figueras (Universidad Carlos III de Madrid); Roberto Hernán González (Economic Science Institute, Chapman University); Praveen Kujal (Universidad Carlos III de Madrid) |
| Abstract: | Several situations in our daily interactions are characterized by uncertainty and asymmetric information regarding the final outcomes. For example, an investor may overstate a project’s value, or a superior may choose to under, or over, state the gains from a project to a subordinate. We modify the standard investment game to study the effect of possible deception, i.e. over-, or under-, statement of the true value, on investee (and investor) behavior. We find that deception is prevalent and around 66% of the investors send false messages. Investors both over-, and under-, state the true value of the multiplier, k. We elicit investee beliefs and find that investees are naive in that almost half of them believe the message they receive. Meanwhile, a large proportion of investors think that sending a message was useful. The introduction of the possibility of deception does not affect trust or trustworthiness on average, but deceivers make the deceived worse off, return less and are more likely to report lying to avoid harming others. Finally, an increase in information asymmetry increases deception. |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:12-23&r=gth |
| By: | Irma Clots-Figueras; Roberto Hernán; Praveen Kujal |
| Abstract: | Several situations in our daily interactions are characterized by uncertainty and asymmetric information regarding the final outcomes. For example, an investor may overstate a project’s value, or a superior may choose to under, or over, state the gains from a project to a subordinate. We modify the standard investment game to study the effect of possible deception, i.e. over-, or under-, statement of the true value, on investee (and investor) behavior. We find that deception is prevalent and around 66% of the investors send false messages. Investors both over-, and under-, state the true value of the multiplier, k. We elicit investee beliefs and find that investees are naive in that almost half of them believe the message they receive. Meanwhile, a large proportion of investors think that sending a message was useful. The introduction of the possibility of deception does not affect trust or trustworthiness on average, but deceivers make the deceived worse off, return less and are more likely to report lying to avoid harming others. Finally, an increase in information asymmetry increases deception |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:cte:werepe:we1227&r=gth |
| By: | Santiago R. Balseiro (Graduate School of Business, Columbia University); Omar Besbes (Graduate School of Business, Columbia University); Gabriel Y. Weintraub (Graduate School of Business, Columbia University) |
| Abstract: | Ad Exchanges are emerging Internet markets where advertisers may purchase display ad placements, in real-time and based on specific viewer information, directly from publishers via a simple auction mechanism. Advertisers join these markets with a pre-specified budget and participate in multiple second-price auctions over the length of a campaign. This paper studies the competitive landscape that arises in Ad Exchanges and the implications for publishers' decisions. Our first main contribution is to introduce the novel notion of a Fluid Mean Field Equilibrium (FMFE) that is behaviorally appealing, computationally tractable, and in some important cases yields a closed-form characterization. Moreover, we show that a FMFE approximates well the rational behavior of advertisers in large markets. Our second main contribution is to use this framework to provide sharp prescriptions for key auction design decisions that publishers face in these markets, such as the reserve price, the allocation of impressions to the exchange versus an alternative channel, and the disclosure of viewers' information. Notably, we show that proper adjustment of the reserve price is key in (1) making profitable for the publisher to try selling all impressions in the exchange before utilizing the alternative channel; and (2) compensating for the thinner markets created by greater disclosure of viewers' information. |
| Keywords: | auction design, revenue management, ad exchange, display advertising, internet, budget constraints, dynamic games, mean field, fl uid approximation |
| JEL: | C73 L86 |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:net:wpaper:1211&r=gth |
| By: | Martijn A. Han; ; ; |
| Abstract: | Fershtman and Judd (1987) and Sklivas (1987) show that strategic delegation reduces firm profits in the one-shot Cournot game. Allowing for infinitely repeated interaction, strategic delegation can increase firm profits as it improves cartel stability. |
| Keywords: | strategic delegation, collusion, cartel stability |
| JEL: | D43 L13 L20 L41 |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2012-056&r=gth |
| By: | Alp Atakan; Mehmet Ekmekci |
| Abstract: | We study a market in which k identical and indivisible objects are allocated using a uniform-price auction where n > k bidders each demand one object. Before the auction, each bidder receives an informative but imperfect signal about the state of the world. The good that is auctioned is a common-value object for the bidders, and a bidder’s valuation for the object is determined jointly by the state of the world and an action that he chooses after winning the object but before he observes the state. We show that there are equilibria in which the auction price is completely uninformative about the state of the world and aggregates no information even in an arbitrarily large auction. In the equilibrium that we construct, because prices do not aggregate information, agents have strict incentives to acquire costly information before they participate in the market. Also, market statistics other than price, such as the amount of rationing and bid distributions contain extra information about the state. Our findings sharply contrast with past work which shows that in large auctions where there is no ex-post action, the auction price aggregates information. |
| Keywords: | Auctions, Large markets, Information Aggregation JEL Classification Numbers: C73, D44, D82, D83. |
| Date: | 2012–10–10 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1553&r=gth |
| By: | Midjord, Rune |
| Abstract: | We consider a job contest in which candidates go through interviews (cheap talk) and are subject to reference checks. We show how competitive pressure - increasing the ratio of "good" to "bad" type candi- dates - can lead to a vast increase in lying and in some cases make bad hires more likely. As the number of candidates increases, it becomes harder to in- duce truth-telling. The interview stage becomes redundant if the candidates, a priori, know each others' type or the result of their own reference check. Finally, we show that the employer can bene t from committing not to reject all the applicants. |
| Keywords: | job contest, cheap talk, commitment |
| JEL: | D82 L20 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:ehu:dfaeii:8770&r=gth |