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on Game Theory |
| By: | Michela Chessa (Université Côte d'Azur, France; GREDEG CNRS); Nobuyuki Hanaki (Osaka University,); Aymeric Lardon (GATE Lyon Saint-Etienne,); Takashi Yamada (Yamaguchi University, Japan) |
| Abstract: | We experimentally compare two well-known mechanisms inducing the Shapley value as an ex ante equilibrium outcome of a noncooperative bargaining procedure: the demand-based Winter's demand commitment bargaining mechanism and the offer-based Hart and Mas-Colell bidding procedure. Our results suggest that, on the one hand, the offer-based Hart and Mas-Colell mechanism better induces players to cooperate and to agree on an efficient outcome; on the other hand, the demand-based Winter mechanism better implements allocations that reflect players' effective bargaining power. |
| Keywords: | Nash Program, Bargaining procedures, Shapley value, Experiments |
| JEL: | C71 C72 C90 D82 |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:gre:wpaper:2021-07&r=all |
| By: | Anne-Christine Barthel (Department of Economics, West Texas A&M University, Canyon, TX 79016, USA); Eric Hoffmann (Department of Economics, West Texas A&M University, Canyon, TX 79016, USA); Tarun Sabarwal (Department of Economics, University of Kansas, Lawrence, KS 66045, USA) |
| Abstract: | The concepts of p-dominance and its generalizations are useful to understand equilibrium selection and equilibrium stability in games. We prove that in games with strategic complements, games with strategic substitutes, and games with combinations of both, these concepts are logically equivalent to pure strategy Nash equilibria in a transformed game of complete information. The transformation process is easy to follow and implement and retains a natural connection to the original game. Therefore, our results make these solution concepts more tractable and accessible, and this is shown in many applications. The connection to Nash equilibrium helps us prove new results about the structure of classes of such solution concepts. Similar to the case of Nash equilibrium, these classes are complete lattices in games with strategic complements, but are totally unordered when we deviate from this case. |
| Keywords: | p-dominance, p-best response set, minimal p-best response set, strategic complements, strategic substitutes |
| JEL: | C62 C72 |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:kan:wpaper:202109&r=all |
| By: | Furkan Sezer; Hossein Khazaei; Ceyhun Eksin |
| Abstract: | We consider linear-quadratic Gaussian (LQG) games in which players have quadratic payoffs that depend on the players' actions and an unknown payoff-relevant state, and signals on the state that follow a Gaussian distribution conditional on the state realization. An information designer decides the fidelity of information revealed to the players in order to maximize the social welfare of the players or reduce the disagreement among players' actions. Leveraging the semi-definiteness of the information design problem, we derive analytical solutions for these objectives under specific LQG games. We show that full information disclosure maximizes social welfare when there is a common payoff-relevant state, when there is strategic substitutability in the actions of players, or when the signals are public. Numerical results show that as strategic substitution increases, the value of the information disclosure increases. When the objective is to induce conformity among players' actions, hiding information is optimal. Lastly, we consider the information design objective that is a weighted combination of social welfare and cohesiveness of players' actions. We obtain an interval for the weights where full information disclosure is optimal under public signals for games with strategic substitutability. Numerical solutions show that the actual interval where full information disclosure is optimal gets close to the analytical interval obtained as substitution increases. |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2102.13047&r=all |
| By: | Christian Ewerhart (Department of Economics, University of Zurich); Dan Kovenock (Economic Science Institute, Chapman University) |
| Abstract: | In this paper, we study N-player Colonel Blotto games with incomplete information about battlefield valuations. Such games arise in job markets, research and development, electoral competition, security analysis, and conflict resolution. For M N + 1 battlefields, we identify a Bayes-Nash equilibrium in which the resource allocation to a given battleÖeld is strictly monotone in the valuation of that battlefield. We also explore extensions such as heterogeneous budgets, the case M N, full-support type distributions, and network games. |
| Keywords: | Colonel Blotto games, Private information, Bayes-Nash equilibrium, Generalized Dirichlet distributions, Networks |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:21-01&r=all |
| By: | Alfred Galichon; Marc Henry |
| Abstract: | We propose a computationally feasible way of deriving the identified features of models with multiple equilibria in pure or mixed strategies. It is shown that in the case of Shapley regular normal form games, the identified set is characterized by the inclusion of the true data distribution within the core of a Choquet capacity, which is interpreted as the generalized likelihood of the model. In turn, this inclusion is characterized by a finite set of inequalities and efficient and easily implementable combinatorial methods are described to check them. In all normal form games, the identified set is characterized in terms of the value of a submodular or convex optimization program. Efficient algorithms are then given and compared to check inclusion of a parameter in this identified set. The latter are illustrated with family bargaining games and oligopoly entry games. |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2102.12249&r=all |
| By: | Ratul Lahkar (Ashoka University); Sayan Mukherjee (Indian Statistical Institute, Kolkata); Souvik Roy (Indian Statistical Institute, Kolkata) |
| Abstract: | We consider a generalization of perturbed best response dynamics in population games with a continuum of strategies. The previous literature has considered the logit dynamic generated through the Shannon entropy as a deterministic perturbation. We consider a wider class of deterministic perturbations satisfying lower semicontinuity and strong convexity. Apart from the Shannon entropy, Tsallis entropy and Burg entropy are other perturbations that satisfy these conditions. We thereby generate the generalized perturbed best response dynamic with a continuum of strategies. We establish fundamental properties of the dynamic and show convergence in potential games and negative semidefinite games. |
| Keywords: | Perturbed Best Response; Logit Dynamic; Potential Games; Negative Semidefinite Games |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:ash:wpaper:51&r=all |
| By: | Heap, Shaun Hargreaves; Ismail, Mehmet |
| Abstract: | Rational players in game theory are neoliberal in the sense that they can choose any available action so as to maximize their payoffs. It is well known that this can result in Pareto inferior outcomes (e.g. the Prisoner's Dilemma). Classical liberalism, in contrast, argues that people should be constrained by a no-harm principle (NHP) when they act. We show, for the first time to the best of our knowledge, that rational players constrained by the NHP will produce Pareto efficient outcomes in n-person non-cooperative games. We also show that both rationality and the NHP are required for this result. |
| Date: | 2021–01–23 |
| URL: | http://d.repec.org/n?u=RePEc:osf:socarx:mgqh7&r=all |
| By: | Johannes Hoelzemann (Department of Economics, University of Toronto); Hongyi Li (School of Economics, UNSW Business School) |
| Abstract: | Motivated by the problem of organizational design, we study coordination in the network minimum game: a version of the minimum-effort game where players are connected by a directed network. We show experimentally that acyclic networks such as hierarchies are most conducive to successful coordination. Introducing a single link to complete a network cycle may drastically inhibit coordination. Further, acyclic networks enable resilient coordination: initial coordination failure is often overcome (exacerbated) after repeated play in acyclic (cyclic) networks. |
| Keywords: | organizational design, weak-link game, minimum-effort game, coordination failure, quantal response equilibrium |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:swe:wpaper:2021-02&r=all |
| By: | Hamid Aghadadashli; Georg Kirchsteiger; Patrick Legros |
| Abstract: | The paper studies the effectiveness of communication in a two-player two-sided asymmetric information context. Both players choose simultaneously between two actions, with action L leading to a lower payoff for the co-player than action H. There are two types of players: D-types for whom L is dominant, and C-types for whom the optimal action is the same as the one chosen by the co-player, with both player choosing H providing the C-type a higher payoff than both players choosing L. Before the actions are chosen, each player can signal his/her intention to choose H. We consider three communication environments: No communication (NC), cheap talk (CT), and an environment with extrinsic communication costs (FC). According to standard theory the range of equilibrium payoffs of both types is the same in NC and CT, while for C-types the equilibrium payoff is highest in FC due to the Spence mechanism (Spence 1973). When we tested these predictions experimentally, the C-type payoffs were the highest in CT. In this environment the average observed C-type Payoff was even higher than the maximum equilibrium payoff. In CT about half of the D-types did not mimic the communication behavior of C-types, and hence even cheap talk revealed some information to the C-types. This indicates that half of the D-types were reluctant to make promises they would break. We introduce a theoretical model with promise-keepers. When the probability of an agent being promise-keeper is around 50%, the signaling rate will be higher in CT than in FC. On the other hand, for the same signal structure C-types choose more often H in the FC than in CT. These predictions are confirmed by the experimental results. Overall, the effect of the higher signalling rate in CT dominates: Together with presence of promise-keepers the higher signalling rate allows the C-types to coordinate more often on the « good » (H;H) outcome in CT, resulting in higher C-type payoffs in CT than in FC. |
| Keywords: | credible communication, asymmetric information, coordination |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/319773&r=all |
| By: | Dengji Zhao |
| Abstract: | Mechanism design has traditionally assumed that the set of participants are fixed and known to the mechanism (the market owner) in advance. However, in practice, the market owner can only directly reach a small number of participants (her neighbours). Hence the owner often needs costly promotions to recruit more participants in order to get desirable outcomes such as social welfare or revenue maximization. In this paper, we propose to incentivize existing participants to invite their neighbours to attract more participants. However, they would not invite each other if they are competitors. We discuss how to utilize the conflict of interest between the participants to incentivize them to invite each other to form larger markets. We will highlight the early solutions and open the floor for discussing the fundamental open questions in the settings of auctions, coalitional games, matching and voting. |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2102.10347&r=all |
| By: | Dufwenberg, Martin; Servátka, Maroš; Tarrasó, Jorge; Vadovič, Radovan |
| Abstract: | Lab evidence on trust games involves more cooperation than conventional economic theory predicts. We explore whether this pattern extends to a field setting where (much like in a lab) we are able to control for (lack of) repeat-play and reputation: cab drivers in Mexico City. We find a remarkably high degree of trustworthiness, also with price-haggling, which is predicted to reduce trustworthiness. |
| Keywords: | trust, honesty, reciprocity, field experiment, haggling, taxis |
| JEL: | C72 C90 C93 |
| Date: | 2021–02–22 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:106256&r=all |
| By: | You Zu; Krishnamurthy Iyer; Haifeng Xu |
| Abstract: | We study a repeated persuasion setting between a sender and a receiver, where at each time $t$, the sender observes a payoff-relevant state drawn independently and identically from an unknown prior distribution, and shares state information with the receiver, who then myopically chooses an action. As in the standard setting, the sender seeks to persuade the receiver into choosing actions that are aligned with the sender's preference by selectively sharing information about the state. However, in contrast to the standard models, the sender does not know the prior, and has to persuade while gradually learning the prior on the fly. We study the sender's learning problem of making persuasive action recommendations to achieve low regret against the optimal persuasion mechanism with the knowledge of the prior distribution. Our main positive result is an algorithm that, with high probability, is persuasive across all rounds and achieves $O(\sqrt{T\log T})$ regret, where $T$ is the horizon length. The core philosophy behind the design of our algorithm is to leverage robustness against the sender's ignorance of the prior. Intuitively, at each time our algorithm maintains a set of candidate priors, and chooses a persuasion scheme that is simultaneously persuasive for all of them. To demonstrate the effectiveness of our algorithm, we further prove that no algorithm can achieve regret better than $\Omega(\sqrt{T})$, even if the persuasiveness requirements were significantly relaxed. Therefore, our algorithm achieves optimal regret for the sender's learning problem up to terms logarithmic in $T$. |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2102.10156&r=all |
| By: | Santiago Balseiro; Christian Kroer; Rachitesh Kumar |
| Abstract: | The internet advertising market is a multi-billion dollar industry, in which advertisers buy thousands of ad placements every day by repeatedly participating in auctions. In recent years, the industry has shifted to first-price auctions as the preferred paradigm for selling advertising slots. Another important and ubiquitous feature of these auctions is the presence of campaign budgets, which specify the maximum amount the advertisers are willing to pay over a specified time period. In this paper, we present a new model to study the equilibrium bidding strategies in first-price auctions for advertisers who satisfy budget constraints on average. Our model dispenses with the common, yet unrealistic assumption that advertisers' values are independent and instead assumes a contextual model in which advertisers determine their values using a common feature vector. We show the existence of a natural value-pacing-based Bayes-Nash equilibrium under very mild assumptions, and study its structural properties. Furthermore, we generalize the existence result to standard auctions and prove a revenue equivalence showing that all standard auctions yield the same revenue even in the presence of budget constraints. |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2102.10476&r=all |
| By: | Geoffroy de Clippel; Rene Saran; Roberto Serrano |
| Abstract: | In de Clippel, Saran, and Serrano (2019), it is shown that, perhaps surprisingly, the set of implementable social choice functions is essentially the same whether agents have bounded depth of reasoning or rational expectations. The picture is quite different when taking into account the possibility of small modeling mistakes. While continuous strict implementation becomes very demanding (Oury and Tercieux (2012) Ð OT), continuity in level-k implementation obtains essentially for free. A decomposition of the conditions implied by the OT implementation notion confirms that it is the use of equilibrium, and not continuity per se, that is responsible for the difference. |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:bro:econwp:2021-002&r=all |
| By: | Erik O. Kimbrough (Smith Institute for Political Economy & Philosophy, Chapman University); David Porter (Economic Science Institute, Chapman University); Mark Schneider (University of Alabama) |
| Abstract: | Evidence from psychology and marketing suggests that those who make a "precise" first offer in bargaining get a better deal than those who make a "round" first offer. We report on a series of experiments designed to test for and improve our understanding of the "precise first offer" (PFO) effect in bargaining and whether it likely reflects rational optimizing or equilibrium behavior. Our experimental treatments vary whether decisions are incentivized and whether the PFO effect can emerge as an equilibrium of a cheap-talk signaling game. We find evidence of a PFO effect when subjects read a vignette and make unincentivized individual decisions. When monetary incentives are added to the vignette, we still find the PFO effect, but it is not robust. In a bilateral bargaining situation with a cheap-talk equilibrium, we can not find the PFO effect, which is inconsistent with the equilibrium predictions. Moreover, the PFO effect reemerges in a setting in which initial offers are generated by a random device and thus provides a strong refutation of the signaling model. Our evidence suggests that optimizing and equilibrium accounts of the PFO effect are inadequate. Understanding initial offers as reference points, which subtly change perceptions about the kinds of acceptable counteroffers, provides a plausible account of a new finding on which prior explanations are silent: precise offers induce more precise counteroffers. |
| Keywords: | bargaining, precise first offers, reference points |
| JEL: | C7 C9 D9 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:20-42&r=all |
| By: | Semyon Malamud; Anna Cieslak; Andreas Schrimpf |
| Abstract: | We study the general problem of optimal information design with continuous actions and continuous state space in arbitrary dimensions. First, we show that with a finite signal space, the optimal information design is always given by a partition. Second, we take the limit of an infinite signal space and characterize the solution in terms of a Monge-Kantorovich optimal transport problem with an endogenous information transport cost. We use our novel approach to: 1. Derive necessary and sufficient conditions for optimality based on Bregman divergences for non-convex functions. 2. Compute exact bounds for the Hausdorff dimension of the support of an optimal policy. 3. Derive a non-linear, second-order partial differential equation whose solutions correspond to regular optimal policies. |
| Date: | 2021–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2102.10909&r=all |
| By: | Florian Ederer (Cowles Foundation, Yale University); Weicheng Min (Yale Department of Economics) |
| Abstract: | We consider a model of Bayesian persuasion in which the Receiver can detect lies with positive probability. We show that the Sender lies more when the lie detection probability increases. As long as the lie detection probability is sufficiently small the Sender’s and the Receiver’s equilibrium payoffs are unaffected by the lie detection technology because the Sender simply compensates by lying more. When the lie detection probability is sufficiently high, the Sender’s (Receiver’s) equilibrium payoff decreases (increases) with the lie detection probability. |
| Keywords: | Bayesian persuasion, Lying, Communication, Lie detection |
| JEL: | D83 D82 K40 D72 |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2272&r=all |