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on Game Theory |
| By: | Stephen Morris (Princeton University); Ming Yang (Duke University) |
| Abstract: | We study a coordination game where players simultaneously acquire information prior to the play of the game. We allow general information acquisition technologies, modeled by a cost functional mapping from information structures. Costly local distinguishability is a property requiring that the cost of distinguishing nearby states is hard relative to distinguishing distant states. This property is not important in decision problems, but is crucial in determining equilibrium outcomes in games. If it holds, there is a unique equilibrium; if it fails, there are multiple equilibria close to those that would exist if there was complete information. We study these issues in the context of a regime change game with a continuum of players. We also provide a common belief foundation for equilibria of this game. This allows us to distinguish cases where the players could (physically) acquire information giving rise to multiple equilibria, but choose not to, and situations where players could not physically have acquired information in a way consistent with multiple equilibria. Our analysis corresponds to the former case, while the choosing precision of additive noise corresponds to the latter case. |
| Keywords: | coordination, endogenous information acquisition, costly local distinguishability, higher order beliefs |
| JEL: | C72 D82 |
| Date: | 2016–05 |
| URL: | http://d.repec.org/n?u=RePEc:pri:metric:079_2016&r=gth |
| By: | Dilip Abreu (Princeton University); Benjamin Brooks (Becker Friedman Institute and Univ ersity of Chicago); Yuliy Sannikov (Princeton University) |
| Abstract: | We study the subgame perfect equilibria of two player stochastic games with perfect monitoring and geometric discounting. A novel algorithm is developed for calculating the discounted payoffs that can be attained in equilibrium. This algorithm generates a sequence of tuples of payoffs vectors, one payoff for each state, that move around the equilibrium payoff sets in a clockwise manner. The trajectory of these "pivot" payoffs asymptotically traces the boundary of the equilibrium payoff correspondence. We also provide an implementation of our algorithm, and preliminary simulations indicate that it is more efficient than existing methods. The theoretical results that underlie the algorithm also yield a bound on the number of extremal equilibrium payoffs. |
| JEL: | C63 C72 C73 D90 |
| Date: | 2016–02 |
| URL: | http://d.repec.org/n?u=RePEc:pri:metric:78_2016&r=gth |
| By: | Dirk Bergemann (Yale University); Stephen Morris (Princeton University) |
| Abstract: | Fixing a game with uncertain payoffs, information design identifies the information structure and equilibrium that maximizes the payoff of an information designer. We show how this perspective unifies existing work, including that on communication in games (Myerson (1991)), Bayesian persuasion (Kamenica and Gentzkow (2011)) and some of our own recent work. Information design has a literal interpretation, under which there is a real information designer who can commit to the choice of the best information structure (from her perspective) for a set of participants in a game. We emphasize a metaphorical interpretation, under which the information design problem is used by the analyst to characterize play in the game under many different information structures. |
| JEL: | C72 C82 D83 C79 |
| Date: | 2016–12 |
| URL: | http://d.repec.org/n?u=RePEc:pri:metric:086_2016&r=gth |
| By: | Dirk Bergemann (Yale University); Stephen Morris (Princeton University) |
| Abstract: | Fixing a game with uncertain payoffs, information design identifies the information structure and equilibrium that maximizes the payoff of an information designer. We show how this perspective unifies existing work, including that on communication in games (Myerson (1991)), Bayesian persuasion (Kamenica and Gentzkow (2011)) and some of our own recent work. Information design has a literal interpretation, under which there is a real information designer who can commit to the choice of the best information structure (from her perspective) for a set of participants in a game. We emphasize a metaphorical interpretation, under which the information design problem is used by the analyst to characterize play in the game under many different information structures. |
| Keywords: | Information design, Bayesian persuasion, correlated equilibrium, incomplete informa- tion, robust predictions, information structure |
| JEL: | C72 D82 D83 |
| Date: | 2017–02 |
| URL: | http://d.repec.org/n?u=RePEc:pri:metric:089_2017&r=gth |
| By: | Stephen Morris (Princeton University); Ming Yang (Duke University) |
| Abstract: | We study a coordination game where players choose what information to acquire about payoffs prior to the play of the game. We allow general information acquisition technologies, modeled by a cost functional defined on information structures. A cost functional satisfies continuous choice if players choose a continuous decision rule even in a decision problem with discontinuous payoffs. If continuous choice holds, there is a unique equilibrium; if it fails, there are multiple equilibria. We show how continuous choice captures the idea that it is sufficiently harder to distinguish states that are close to each other relative to far away states. |
| Keywords: | coordination, endogenous information acquisition, continuous choice, higher order beliefs |
| JEL: | C72 D82 |
| Date: | 2016–12 |
| URL: | http://d.repec.org/n?u=RePEc:pri:metric:087_2017&r=gth |
| By: | Stephen Morris (Princeton University); Hyun Song Shin (Bank for International Settlements); Muhamet Yildiz (M.I.T.) |
| Abstract: | We study coordination games under general type spaces. We characterize rationalizable actions in terms of the properties of the belief hierarchies and show that there is a unique rationalizable action played whenever there is approximate common certainty of rank beliefs, defined as the probability the players assign to their payoff parameters being higher than their opponents'. We argue that this is the driving force behind selection results for the specific type spaces in the global games literature. |
| JEL: | C70 D83 |
| Date: | 2015–11 |
| URL: | http://d.repec.org/n?u=RePEc:pri:metric:069_2015&r=gth |
| By: | Paula Jaramillo; Ça?atay Kay?; Flip Klijn |
| Abstract: | We consider school choice problems (Abdulkadiro?lu and Sönmez, 2003) where students are assigned to public schools through a centralized assignment mechanism. We study the family of so-called rank-priority mechanisms, each of which is induced by an order of rank-priority pairs. Following the corresponding order of pairs, at each step a rank-priority mechanism considers a rank-priority pair and matches an available student to an unfilled school if the student and the school rank and prioritize each other in accordance with the rank-priority pair. The Boston or immediate acceptance mechanism is a particular rank-priority mechanism. Our first main result is a characterization of the subfamily of rank-priority mechanisms that Nash implement the set of stable (i.e., fair) matchings (Theorem 1). We show that our characterization also holds for “sub-implementation” and “sup-implementation” (Corollaries 3 and 4). Our second main result is a strong impossibility result: under incomplete information, no rank-priority mechanism implements the set of stable matchings (Theorem 2). |
| Keywords: | School choice; rank-priority mechanisms; stability; Nash implementation |
| JEL: | C78 D61 D78 I20 |
| Date: | 2017–03–02 |
| URL: | http://d.repec.org/n?u=RePEc:col:000092:015501&r=gth |
| By: | Dirk Bergemann (Yale University); Stephen Morris (Princeton University) |
| Abstract: | A set of players have preferences over a set of outcomes. We consider the problem of an "information designer" who can choose an information structure for the players to serve his ends, but has no ability to change the mechanism (or force the players to make particular action choices). We describe a unifying perspective for information design. We consider a simple example of Bayesian persuasion with both an uninformed and informed receiver. We extend information design to many player and relate it to the literature on incomplete information correlated equilibrium. |
| Keywords: | Information Design, Bayesian Persuasion, Bayes Correlated Equilibrium, Information Structure |
| JEL: | D82 D83 C72 |
| Date: | 2016–01 |
| URL: | http://d.repec.org/n?u=RePEc:pri:metric:076_2016&r=gth |
| By: | Dirk Bergemann (Yale University); Benjamin Brooks (University of Chicago); Stephen Morris (Princeton University) |
| Abstract: | We study auction design when bidders have a pure common value equal to the maximum of their independent signals. In the revenue maximizing mechanism, each bidder makes a payment that is independent of his signal and the allocation discriminates in favor of bidders with lower signals. We provide a necessary and sufficient condition under which the optimal mechanism reduces to a posted price under which all bidders are equally likely to get the good. This model of pure common values can equivalently be interpreted as model of resale: the bidders have independent private values at the auction stage, and the winner of the auction can make a take-it-or-leave-it-offer in the secondary market under complete information. |
| JEL: | C72 D44 D82 D83 |
| Date: | 2016–12 |
| URL: | http://d.repec.org/n?u=RePEc:pri:metric:085_2016&r=gth |
| By: | Paula Jaramillo; Ça?atay Kayi; Flip Klijn |
| Abstract: | This paper deals with roommate problems (Gale and Shapley, 1962) that are solvable, i.e., have a non-empty core (set of stable matchings). We study the assortativeness of stable matchings and the size of the core by means of maximal and average rank gaps. We provide upper bounds in terms of maximal and average disagreements in the agents’ rankings. Finally, we show that most of our bounds are tight. |
| Keywords: | Matching, roommate problem, stability, core, rank gap, bound |
| JEL: | C78 |
| Date: | 2017–02–28 |
| URL: | http://d.repec.org/n?u=RePEc:col:000092:015499&r=gth |
| By: | Llorente-Saguer, Aniol; Zultan, Ro'i |
| Abstract: | The theoretical literature on collusion in auctions suggests that the first-price mechanism can deter the formation of bidding rings. However, such analyses neglect to consider the effects of failed collusion attempts, wherein information revealed in the negotiation process may affect bidding behavior. We experimentally test a setup in which theory predicts no collusion and no information revelation in first-price auctions. The results reveal a hitherto overlooked failing of the first-price mechanism: failed collusion attempts distort bidding behavior, resulting in a loss of seller revenue and efficiency. Moreover, the first-price mechanism does not result in less collusion than the second-price mechanism. We conclude that, while the features of the first-price mechanism may have the potential to deter bidder collusion, the role of beliefs in guiding bidding behavior make it highly susceptible to distortions arising from the informational properties of collusive negotiation. Auction designers should take this phenomenon into account when choosing the auction mechanism. |
| Keywords: | auctions; Collusion; Experiment |
| JEL: | C72 C91 D44 |
| Date: | 2017–03 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:11944&r=gth |
| By: | Josue Ortega |
| Abstract: | We study the random multi-unit assignment problem in which the number of goods to be distributed depends on players' preferences, obtaining several results that also apply to its corresponding version with fixed number of goods, commonly referred to as the course allocation problem. Although efficiency, envy-freeness, and group strategy-proofness can be achieved in the domain of dichotomous preferences, two standard results disappear: the egalitarian solution cannot be supported by competitive prices, so the competitive solution can no longer be computed with the Eisenberg-Gale program maximizing the Nash product, and the competitive allocation with equal incomes is no longer unique. The egalitarian solution is more appealing than the competitive one in this setup because it is Lorenz dominant, unique, and impossible to manipulate by groups. Moreover, it can be adapted to satisfy a new fairness axiom that arises naturally in this context. |
| Date: | 2017–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1703.10897&r=gth |
| By: | Benyamin Shitovitz (University of Haifa, Department of Economics); Avishay Aiche (Faculty of Industrial Engineering and Management, Technion) |
| Keywords: | Game theory, Pollution, Core, Pareto Domination |
| JEL: | C71 C72 |
| URL: | http://d.repec.org/n?u=RePEc:haf:huedwp:wp201606&r=gth |
| By: | Dirk Bergemann (Yale University); Benjamin Brooks (University of Chicago); Stephen Morris (Princeton University) |
| Abstract: | A single unit of a good is to be sold by auction to one of two buyers. The good has either a high value or a low value, with known prior probabilities. The designer of the auction knows the prior over values but is uncertain about the correct model of the buyers' beliefs. The designer evaluates a given auction design by the lowest expected revenue that would be generated across all models of buyers' information that are consistent with the common prior and across all Bayesian equilibria. An optimal auction for such a seller is constructed, as is a worst-case model of buyers' information. The theory generates upper bounds on the seller's optimal payoff for general many-player and common-value models. |
| Keywords: | Optimal auctions, common values, information structure, mo del uncertainty, ambiguity aversion, robustness, Bayes correlated equilibrium, revenue maximization, revenue equivalence, information rent |
| JEL: | C72 D44 D82 D83 |
| Date: | 2016–12 |
| URL: | http://d.repec.org/n?u=RePEc:pri:metric:084_2016&r=gth |
| By: | Gisèle Umbhauer |
| Abstract: | The paper is about mixed strategy Nash equilibria in discrete second price all-pay auctions with a limit budget. Two players fight over a prize of value V. Each player submits a bid lower or equal to M, the limit budget. The prize goes to the highest bidder but both bidders pay the lowest bid. V, M and the bids are integers. The paper studies the convergence of the mixed Nash equilibrium probability distribution in the discrete auction to the mixed Nash equilibrium probability distribution in the more well-known continuous second price all-pay auction –or static war of attrition. We establish that the- expected- convergence between discrete and continuous equilibrium distributions is in no way automatic. Both distributions converge for V odd and large, but, for even values of V, the discrete distribution is quite strange and obeys a singular yoyo phenomenon: the probabilities assigned to two adjacent bids are quite different, one probability being much lower than the continuous one, the adjacent probability being much larger. So the discrete probabilities, for V even, don’t converge to the continuous ones. Yet there is a convergence, when turning to sums: the sums of the discrete probabilities of two adjacent bids converge to the sums of the continuous probabilities of the same two bids for large values of V. It is shown in the paper that the yoyo phenomenon doesn’t disappear - it is even strengthened- when switching to lower natural bid increments, like 0.5 or 0.1. More generally, it is shown that convergence is an exception rather than the rule and that it requires a special link between V, M and the bid increment. It follows a lack of continuity between the discrete Nash equilibria and the continuous Nash equilibria. |
| Keywords: | discrete game, continuous game, second price all-pay auction, Nash equilibrium, increment. |
| JEL: | C72 D44 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:ulp:sbbeta:2017-14&r=gth |
| By: | Sonja Brangewitz (Paderborn University); Behnud Mir Djawadi (Paderborn University); Angelika Endres (Paderborn University); Britta Hoyer (Paderborn University) |
| Abstract: | We experimentally study the emergence of networks under a known external threat. To be more specific, we deal with the question if subjects in the role of a strategic Designer are able to form safe and efficient networks while facing a strategic Adversary who is going to attack their networks. This investigation relates theoretical predictions by Dziubinski and Goyal (2013) to actual observed behaviour. Varying the costs for protecting nodes, we designed and tested two treatments with different predictions for the equilibrium network. Furthermore, the in fluence of the subjects' farsightedness on their decision- making process was elicited and analysed. We find that while subjects are able to build safe networks in both treatments, equilibrium networks are only built in one of the two treatments. In the other treatment, predominantly safe networks are built but they are not efficient. Additionally, we find that farsightedness -as measured in our experiment- has no in fluence on whether subjects are able to build safe or efficient networks. |
| Keywords: | Networks, Experiment, Network Design, Network Defence, Network Disruption |
| Date: | 2017–04 |
| URL: | http://d.repec.org/n?u=RePEc:pdn:ciepap:101&r=gth |
| By: | Alia Gizatulina (University of St. Gallen and Max Planck Institute for Research on Collective Goods); Olga Gorelkina (Max Planck Institute for Research on Collective Goods) |
| Abstract: | We study the division of trade surplus in a competitive market environment by conducting a natural field experiment on German eBay. Acting as a seller, we offer Amazon gift cards with face values of up to 500 Euro. Randomly arriving buyers, the subjects of our experiment, make price offers according to eBay rules. Using a novel decomposition method, we infer offered shares of trade surplus and find that the average share proposed to the seller amounts to 29%. Additionally, we document: (i) insignificant effects of stake size; (ii) poor use of strategically relevant public information; and (iii) behavioural differences between East and West German subjects. |
| Keywords: | Field experiment, ultimatum game, surplus division, bargaining, Internet trade, eBay |
| JEL: | C72 C93 C57 |
| Date: | 2016–12 |
| URL: | http://d.repec.org/n?u=RePEc:mpg:wpaper:2016_20&r=gth |