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on Game Theory |
| By: | Annie Liang |
| Abstract: | This paper proposes a foundation for heterogeneous beliefs in games, in which disagreement arises not because players observe different information, but because they learn from common information in different ways. Players may be misspecified, and may moreover be misspecified about how others learn. The key assumption is that players nevertheless have some common understanding of how to interpret the data; formally, players have common certainty in the predictions of a class of learning rules. The common prior assumption is nested as the special case in which this class is a singleton. The main results characterize which rationalizable actions and Nash equilibria can be predicted when agents observe a finite quantity of data, and how much data is needed to predict various solutions. This number of observations needed depends on the degree of strictness of the solution and speed of common learning. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.07018&r=all |
| By: | Pycia, Marek; Troyan, Peter |
| Abstract: | We introduce a general class of simplicity standards that vary the foresight abilities required of agents in extensive-form games. Rather than planning for the entire future of a game, agents are presumed to be able to plan only for those histories they view as simple from their current perspective. Agents may update their so-called strategic plan as the game progresses, and, at any point, for the called-for action to be simply dominant, it must lead to unambiguously better outcomes, no matter what occurs at non-simple histories. We use our approach to simplicity to provide characterizations of simple mechanisms in general social choice environments both with and without transfers, including canonical mechanisms such as ascending auctions, posted prices, and serial dictatorship-style mechanisms. As a final application, we explain the widespread popularity of the well-known Random Priority mechanism by characterizing it as the unique mechanism that is efficient, fair, and simple to play. |
| JEL: | C72 C78 D44 D82 |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:14043&r=all |
| By: | Godfrey Keller; Sven Rady |
| Abstract: | We analyze undiscounted continuous-time games of strategic experimentation with two-armed bandits. The risky arm generates payoffs according to a Le´vy process with an unknown average payoff per unit of time which nature draws from an arbitrary finite set. Observing all actions and realized payoffs, players use Markov strategies with the common posterior belief about the unknown parameter as the state variable. We show that the unique symmetric Markov perfect equilibrium can be computed in a simple closed form involving only the payoff of the safe arm, the expected current payoff of the risky arm, and the expected full-information payoff, given the current belief. In particular, the equilibrium does not depend on the precise specification of the payoff-generating processes. |
| Keywords: | Strategic Experimentation, Two-Armed Bandit, Strong Long-Run Av¬erage Criterion, Markov Perfect Equilibrium, HJB Equation, Viscosity Solution |
| JEL: | C73 D83 |
| Date: | 2019–10–10 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:882&r=all |
| By: | Francesco Cerigioni; Fabrizio Germano; Pedro Rey-Biel; Peio Zuazo-Garin |
| Keywords: | Rationality, higher-order rationality, revealed rationality, levels of thinking. |
| JEL: | C70 C72 C91 D01 |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:upf:upfgen:1672&r=all |
| By: | Oechssler, Joerg; Reischmann, Andreas; Sofianos, Andis |
| Abstract: | We present a new and simple mechanism for repeated public good environments. In the Conditional Contribution Mechanism (CCM), agents send two message of the form, "I am willing to contribute x units to the public good if in total y units are contributed." This mechanism offers agents risk-free strategies, which we call unexploitable. We prove that if agents choose unexploitable messages in a Better Response Dynamics model, all stable outcomes of the CCM are Pareto efficient. We conduct a laboratory experiment to investigate whether observed behavior is consistent with this prediction. In the complete information case we find that indeed almost 80% of outcomes are Pareto optimal. Furthermore, comparison treatments with the Voluntary Contribution Mechanism show that the CCM leads to significantly higher contribution rates. Even under incomplete information, contributions are fairly high and do not deteriorate over time. |
| Keywords: | Experimental Economics,Public Goods,Mechanism Design,Better Response Dynamics |
| JEL: | C72 C92 D82 H41 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:wzbmbh:spii2019209&r=all |
| By: | Tilman Klumpp; Kai A. Konrad |
| Abstract: | We study Colonel Blotto games with sequential battles and a majoritarian objective. For a large class of contest success functions, the equilibrium is unique and characterized by an even split: Each battle that is reached before one of the players wins a majority of battles is allocated the same amount of resources from the player’s overall budget. As a consequence, a player’s chance of winning any particular battle is independent of the battleï¬ eld and of the number of victories and losses the player accumulated in prior battles. This result is in stark contrast to equilibrium behavior in sequential contests that do not involve either ï¬ xed budgets or a majoritarian objective. We also consider the equilibrium choice of an overall budget. For many contest success functions, if the sequence of battles is long enough the payoff structure in this extended games resembles an all-pay auction without noise. |
| Keywords: | Blotto games, dynamic battles, multi-battle contest, all-pay auctions, sequential elections |
| JEL: | D72 D74 |
| Date: | 2018–06 |
| URL: | http://d.repec.org/n?u=RePEc:mpi:wpaper:tax-mpg-rps-2018-05&r=all |
| By: | Lisa Windsteiger |
| Abstract: | In this paper I develop a general model of how social segregation and beliefs interact. Sorting decisions will be affected by beliefs about society, but these beliefs about society are in turn influenced by social interactions. In my model, people sort into social groups according to income, but become biased about the income distribution once they interact only with their own social circle. I define "biased sorting equilibria", which are stable partitions in which people want to stay in their chosen group, despite their acquired misperceptions about the other groups. I introduce a refinement criterion - the consistency requirement - and find necessary and su¢ cient conditions for existence and uniqueness of biased sorting equilibria. |
| Keywords: | Stratification, Assortative Matching, Group Formation, Beliefs |
| JEL: | D83 D85 Z13 |
| Date: | 2018–10 |
| URL: | http://d.repec.org/n?u=RePEc:mpi:wpaper:tax-mpg-rps-2018-08&r=all |
| By: | Christos Mavridis; Marco Serena |
| Abstract: | In this note, we characterize the equilibria of the standard pivotal-voter participation game between two groups of voters of asymmetric sizes, as originally proposed by Palfrey and Rosenthal [1983. A strategic calculus of voting. Public Choice. 41, 7-53]. |
| Keywords: | Costly voting, pivotal voter model, complete information |
| Date: | 2018–11 |
| URL: | http://d.repec.org/n?u=RePEc:mpi:wpaper:tax-mpg-rps-2018-07&r=all |
| By: | Yannis Bakos (Stern School of Business, New York University); Hanna Halaburda (Stern School of Business, New York University) |
| Abstract: | As the costs of joining platforms decrease, we often see participants in both sides of two-sided platforms to multihome, a case mostly ignored in the literature on competition between two-sided platforms. We help to fill this gap by developing a model for platform competition in a differentiated setting (a Hoteling line), which is similar to other models in the literature but focuses on the case where at least some agents on each side multihome. We show that in that case the strategic interdependence between the two sides of the same platform may be of lesser importance, or even not be present at all, compared to models that assume single-homing on at least one side of the market. The implication is that when multihoming may be present on both sides of the market, the benefit of subsidizing one side (typically the one with higher price elasticity) is diminished or may not be present at all. This outcome differs from most of the two-sided platform literature, where interdependence between the two sides served by the same platform is a major result leading to the policy implication that a platform will often maximize its total profits by subsidizing one side, typically the one with more elastic demand. Our analysis shows that the common strategic advice to subsidize one side in order to maximize total profits may be limited or even incorrect when both sides multihome, which can be significant given the increasing prevalence of multihoming. |
| Keywords: | multihoming, platforms, two-sided platforms, network effects, platform subsidies |
| JEL: | L10 L81 L82 L86 O33 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:net:wpaper:1912&r=all |
| By: | Pierrot, Thibaud |
| Abstract: | An individual is affected by the curse of knowledge when he fails to appreciate the viewpoint of a lesser-informed agent. In contrast to a rational person, the cursed individual behaves as if part of his private information were common knowledge. This systematic cognitive bias alters many predictions derived from game theory which involve an asymmetry of information between the players. We investigate in this article how the curse of knowledge modifies individual behaviours in negotiation situations. We report the results of a laboratory experiment that was designed to isolate the effect of the curse of knowledge by varying the information available to the players ceteris paribus. Our analysis of the expectations and choices of subjects playing the ultimatum game in different information settings indicates that the curse of knowledge can lead to an increase of impasses in the negotiation and partially explains empirically observed phenomenons such as abnormally high rates of bargaining failures. Unlike previous behavioural research, that is mostly based on motivated beliefs and actions, this work provides a purely nonstrategic explanation for negotiation impasses observed in many real life situations. |
| Keywords: | curse of knowledge,hindsight bias,negotiation,experiments |
| JEL: | C91 D80 D82 D83 D84 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:wzbmbh:spii2019211&r=all |
| By: | Gisčle Umbhauer; Arnaud Wolff |
| Abstract: | We introduce a new equilibrium concept, called the individually-consistent sequential equilibrium (ICSE). This concept is more permissive than the sequential equilibrium (Kreps, Wilson (1982)) but more demanding than the self-confirming one (Fudenberg, Levine (1993)). We require that players share common beliefs on the actions planned to be played at all the information sets, but not on the potential deviations. Therefore, in contrast to Kreps, Wilson (1982), we allow different players to have in mind different perturbation systems, or alternative hypotheses. This is motivated by the fact that beliefs about unobserved events are by essence not verifiable. |
| Keywords: | Sequential Equilibrium, Consistency, Perturbations, Beliefs. |
| JEL: | C72 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ulp:sbbeta:2019-39&r=all |
| By: | Luciano Andreozzi (Department of Economics, University of Trento); Matteo Ploner (Department of Economics, University of Trento); Ali Seyhun Saral (Max Planck Institute for Research on Collective Goods, Bonn) |
| Abstract: | An often-replicated result in the experimental literature on social dilemmas is that a large share of subjects reveal conditionally cooperative preferences. Cooperation generated by this type of preferences is notoriously unstable, as individuals reduce their contributions to the public good in reaction to other subjects free-riding. This has led to the widely-shared conclusion that cooperation observed in experiments (and its collapse) is mostly driven by imperfect reciprocity. In this study, we explore the possibility that reciprocally cooperative preferences may themselves be unstable. We do so by observing the evolution of subjects’ preferences in an anonymously repeated social dilemma. Our results show that a significant fraction of reciprocally cooperative subjects become selfish in the course of the experiment, while the reverse is rarely observed. We are thus driven to the conclusion that egoism is more resistant to exposure to social dilemmas than reciprocity. |
| Keywords: | reciprocity, conditional cooperation, strategy method |
| JEL: | C72 C91 |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:mpg:wpaper:2019_12&r=all |
| By: | Weber, Shlomo; Weber, Yuval; Wiesmeth, Hans |
| Abstract: | he paper introduces a model of military alliance financed through its members' contributions. The member countries vary on four dimensions: GDP per capita, population, "awareness of the alliance", and the place in the alliance hierarchy. The latter refers to the situation where some countries can be considered as "leaders" or even "super-leaders" whose contribution decisions determine the response of the "followers". The interaction between the countries is modeled by means of the Penrose-Stackelberg mechanism that yields a unique equilibrium and identifies the factors that determine the patterns of burden-sharing in an alliance. We then apply our theoretical setting to NATO and conduct an empirical investigation of our model. The paper evaluates the differences in burden sharing along political, military, and economic dimensions, specifically NATO's goal for member-states to spend 2% of GDP on defense, and demonstrates that alliance "awareness" and place in the alliance hierarchy due to historical factors can explain whether NATO states meet their burden-sharing goal. |
| Keywords: | Alliances; Burden Sharing; free riding; multi-stage Penrose-Stackelberg equilibrium; NATO; Public Goods |
| JEL: | C72 D62 D74 H41 |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:13965&r=all |
| By: | Doval, Laura; Skreta, Vasiliki |
| Abstract: | We show that posted prices are the optimal mechanism to sell a durable good to a privately informed buyer when the seller has limited commitment in an infinite horizon setting. We provide a methodology for mechanism design with limited commitment and transferable utility. Whereas in the case of commitment, subject to the buyer's truthtelling and participation constraints, the seller's problem is a decision problem, in the case of limited commitment, the seller's problem corresponds to an intrapersonal game, where different "incarnations" of the seller represent the different beliefs he may have about the buyer's valuation. |
| Keywords: | information design; intrapersonal equilibrium; Limited Commitment; mechanism design; posted price; self-generation |
| JEL: | D84 D86 |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:13967&r=all |
| By: | Renaud Foucart; Jana Friedrichsen |
| Abstract: | We study a game in which two firms compete in quality to serve a market consisting of consumers with different initial consideration sets. If both firms invest below a certain quality threshold, they only compete for those consumers already aware of their existence. Above this threshold, a firm is visible to all and the highest quality attracts all consumers. In equilibrium, firms do not choose their investment deterministically but randomize over two disconnected intervals. On the one hand, the existence of initially captive consumers introduces an anti-competitive element: holding fixed the behavior of the rival firm, a firm with a larger captive segment enjoys a higher payoff from not investing at all. On the other hand, the fact that a firm’s initially captive consumers can still be attracted by very high quality introduces a pro-competitive element: high quality investments becomes more profitable for the underdog when the captive segment of the dominant firm increases. The share of initially captive consumers therefore has a non-monotonic effect on the investment levels of both firms. |
| Keywords: | quality competition, all-pay auction, endogenous prize, consideration sets |
| JEL: | D21 D44 M13 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:lan:wpaper:277451127&r=all |