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on Game Theory |
| By: | Takashi Ui (Hitotsubashi University) |
| Abstract: | A linear-quadratic-Gaussian (LQG) game is an incomplete information game with quadratic payoff functions and Gaussian information structures. It has many applications such as a Cournot game, a Bertrand game, a beauty contest game, and a network game among others. LQG information design is a problem to find an information structure from a given collection of feasible Gaussian information structures that maximizes a quadratic objective function when players follow a Bayes Nash equilibrium. This paper studies LQG information design by formulating it as semidefinite programming, which is a natural generalization of linear programming. Using the formulation, we provide sufficient conditions for optimality and suboptimality of no and full information disclosure. In the case of symmetric LQG games, we characterize the optimal symmetric information structure, and in the case of asymmetric LQG games, we characterize the optimal public information structure, each of which is in a closed-form expression. |
| Keywords: | incomplete information games, optimal information structures, information design, Bayesian persuasion. |
| JEL: | C72 D82 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:upd:utmpwp:018&r=all |
| By: | Simon Finster (Nuffield College and Department of Economics, University of Oxford) |
| Abstract: | We study equilibria in Product-Mix, sequential, and simultaneous auctions, which are used to sell differentiated, indivisible goods. A flexible bidder with unit demand, interested in buying any of the goods, competes against several inflexible bidders, each interested in only one specific good. For first-price and second-price payments, we obtain theoretical results on equilibrium bidding, and compare efficiency, revenue, and bidder surplus numerically. Differences in outcomes between Product-Mix and sequential auctions are small for a range of value distributions. The simultaneous auction performs worst in all dimensions, and differences in performance vary substantially with the degree of competition the flexible bidder faces. |
| Keywords: | multi-unit auctions, asymmetric auctions, market power, menu auctions, sequential auctions, simultaneous auctions |
| JEL: | C72 D44 D47 D61 D82 |
| Date: | 2020–03–24 |
| URL: | http://d.repec.org/n?u=RePEc:nuf:econwp:2003&r=all |
| By: | Francesco Cordoni; Fabrizio Lillo |
| Abstract: | We consider the general problem of a set of agents trading a portfolio of assets in the presence of transient price impact and additional quadratic transaction costs and we study, with analytical and numerical methods, the resulting Nash equilibria. Extending significantly the framework of Schied and Zhang (2018), who considered two agents and one asset, we focus our attention on the conditions on the value of transaction cost making the trading profile of the agents, and as a consequence the price trajectory, wildly oscillating and the market unstable. We find that the presence of more assets, the heterogeneity of trading skills (e.g. speed or cost), and a large number of agents make the market more prone to large oscillations and instability. When the number of assets is fixed, a more complex structure of the cross-impact matrix, i.e. the existence of multiple factors for liquidity, makes the market less stable compared to the case when a single liquidity factor exists. |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2004.03546&r=all |
| By: | Qin, Botao |
| Abstract: | This paper uses a beauty contest game to test the gender differences in strategic reasoning. Using both a non-monetary incentive treatment and a monetary incentives treatment in China, I find there are differences in strategic reasoning.However, the differences disappear with the increase of stakes. |
| Keywords: | Gender; Beauty Contest Game |
| JEL: | C72 C91 J16 |
| Date: | 2019–12–06 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:99604&r=all |
| By: | Aditya Aradhye; J\'anos Flesch; Mathias Staudigl; Dries Vermeulen |
| Abstract: | We introduce a model of sender-receiver stopping games, where the state of the world follows an iid--process throughout the game. At each period, the sender observes the current state, and sends a message to the receiver, suggesting either to stop or to continue. The receiver, only seeing the message but not the state, decides either to stop the game, or to continue which takes the game to the next period. The payoff to each player is a function of the state when the receiver quits, with higher states leading to better payoffs. The horizon of the game can be finite or infinite. We prove existence and uniqueness of responsive (i.e. non-babbling) Perfect Bayesian Equilibrium (PBE) under mild conditions on the game primitives in the case where the players are sufficiently patient. The responsive PBE has a remarkably simple structure, which builds on the identification of an easy-to-implement and compute class of threshold strategies for the sender. With the help of these threshold strategies, we derive simple expressions describing this PBE. It turns out that in this PBE the receiver obediently follows the recommendations of the sender. Hence, surprisingly, the sender alone plays the decisive role, and regardless of the payoff function of the receiver the sender always obtains the best possible payoff for himself. |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2004.01910&r=all |
| By: | Maria Gabriella Graziano (Università di Napoli Federico II and CSEF); Maria Laura Pesce (Università di Napoli Federico II and CSEF); Niccolo Urbinati (Università Ca Foscari Venezia) |
| Abstract: | We introduce new notions of bargaining set for mixed economies which rest on the idea of generalized coalitions (Aubin1979) to define objections and counter-objections. We show that the bargaining set defined through generalized coalitions coincides with competitive allocations under assumptions which are weak and natural in the mixed market literature. As a further result, we identify some additional properties that a generalized coalition must satisfy to object an allocation. |
| Keywords: | Coalitions, Generalized Coalitions, Core, Bargainig Set |
| JEL: | D51 D11 D4 |
| Date: | 2020–03–30 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:560&r=all |
| By: | Chen, Jiaqi; Lee, Sang-Ho |
| Abstract: | This paper investigates strategic choices between duopolistic firms’ R&D investments and government’s output subsidies in an endogenous timing game with research spillovers. We show that a simultaneous-move game among three players appears at equilibrium if the spillovers are very low while government leadership with both firms’ simultaneous-move game appears otherwise. We also show that government followership appears unless the spillovers are low or high, while both the government leadership and followership outcomes are socially desirable at quilibrium. However, a single firm’s leadership equilibrium appears if the spillovers are high, but it causes a welfare loss. |
| Keywords: | Endogenous timing game; Research spillovers, R&D investments; Output subsidies; |
| JEL: | H21 L13 |
| Date: | 2020–04–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:99503&r=all |
| By: | Sokolovskyi, Dmytro |
| Abstract: | The subject of this study is the modeling of Race to the bottom to verify, is really Race to the bottom is a kind of Prisoner’s dilemma. The importance of this issue is explained by the following: if Race to the bottom is a kind of Prisoner’s dilemma, achieving equilibrium tax competition two or more economies leads to deterioration of their economic results As a result, governments have to weaken social, environmental, labor standards and norms. At the same time, many statistical studies of real economies do not discover the above consequence of the tax competition, so it is concluded that there is no Race to the bottom. On the other hand, if Race to the bottom is not a kind of PD then that there is no deterioration in standards during the tax competition does not mean that there is no Race to the bottom. Using a game-theoretic model we consider 3 objective functions for government behavior: the investment volume, the budget revenue, and their combination. For each function, there were calculated conditions under which Race to the bottom is a kind of Prisoner’s dilemma. Introduced a concept of tax-investment equilibrium, as a situation in which all economies are equal for the investor. For the tax-investment equilibrium, there were calculated sufficient conditions under which Race to the bottom is a kind of Prisoner’s dilemma. |
| Keywords: | Race to the bottom; Prisoner’s dilemma; tax competition; government behavior; corporate tax rate; game theory; tax-investment equilibrium |
| JEL: | C72 E62 H30 |
| Date: | 2020–04–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:99404&r=all |
| By: | Daniel Bj\"orkegren; Joshua E. Blumenstock; Samsun Knight |
| Abstract: | An increasing number of decisions are guided by machine learning algorithms. In many settings, from consumer credit to criminal justice, those decisions are made by applying an estimator to data on an individual's observed behavior. But when consequential decisions are encoded in rules, individuals may strategically alter their behavior to achieve desired outcomes. This paper develops a new class of estimator that is stable under manipulation, even when the decision rule is fully transparent. We explicitly model the costs of manipulating different behaviors, and identify decision rules that are stable in equilibrium. Through a large field experiment in Kenya, we show that decision rules estimated with our strategy-robust method outperform those based on standard supervised learning approaches. |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2004.03865&r=all |
| By: | Rene van den Brink (Vrije Universiteit Amsterdam); Saish Nevrekar (Universidad Carlos III de Madrid) |
| Abstract: | This paper develops a model of conflict resolution over scarce water in a trans-boundary river. In our model, we consider countries that are located along a river and made a military investment. Given these investments and their location along the river, they sequentially bargain over the surplus of water, or decide to engage in a military conflict with their upstream neighbour. The probability of winning a military conflict is determined by a contest success function which depends on the military investments made before. We speak about a peaceful agreement if the countries rationally decide to bargain over the water instead of engaging into a military conflict. We show that, if all benefit functions are nonnegative, increasing and concave, then for every level of military investment, there always exists a peaceful agreement where every country prefers to bargain peacefully for the water. We provide a scenario that yields one such a peaceful agreement. |
| Keywords: | River sharing, peaceful agreement, contest success function, subgame perfect equilibrium |
| JEL: | C78 D62 D74 Q25 |
| Date: | 2020–04–04 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20200016&r=all |
| By: | Dirk Bergemann; Alessandro Bonatti; Tan Gan |
| Abstract: | A data intermediary pays consumers for information about their preferences and sells the information so acquired to firms that use it to tailor their products and prices. The social dimension of the individual data---whereby an individual's data are predictive of the behavior of others---generates a data externality that reduces the intermediary's cost of acquiring information. We derive the intermediary's optimal data policy and show that it preserves the privacy of the consumers' identities while providing precise information about market demand to the firms. This enables the intermediary to capture the entire value of information as the number of consumers grows large. |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2004.03107&r=all |
| By: | S. Nageeb Ali; Ayal Chen-Zion; Erik Lillethun |
| Abstract: | Information is replicable in that it can be simultaneously consumed and sold to others. We study how resale affects a decentralized market for information. We show that even if the initial seller is an informational monopolist, she captures non-trivial rents from at most a single buyer: her payoffs converge to 0 as soon as a single buyer has bought information. By contrast, if the seller can also sell valueless tokens, there exists a ``prepay equilibrium'' where payment is extracted from all buyers before the information good is released. By exploiting resale possibilities, this prepay equilibrium gives the seller as high a payoff as she would achieve if resale were prohibited. |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2004.01788&r=all |