|
on Game Theory |
| By: | Christian Ewerhart |
| Abstract: | At the time of writing, the Riemann Hypothesis (RH) is one of the major unsolved problems in pure mathematics. In this note, a parameterized family of non-cooperative games is constructed with the property that, if RH holds true, then any game in this family admits a unique Nash equilibrium. |
| Keywords: | Riemann hypothesis, Nash equilibrium |
| JEL: | C72 |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:410&r= |
| By: | Bruno Salcedo; Bruno Sultanum; Ruilin Zhou |
| Abstract: | This paper studies the optimal design of a liability-sharing arrangement as an infinitely repeated game. We construct a noncooperative model with two agents: one active and one passive. The active agent can take a costly and unobservable action to reduce the incidence of crisis, but a crisis is costly for both agents. When a crisis occurs, each agent decides unilaterally how much to contribute mitigating it. For the one-shot game, when the avoidance cost is too high relative to the expected loss of crisis for the active agent, the first-best is not achievable. That is, the active agent cannot be induced to put in effort to minimize the incidence of crisis in a static game. We show that with the same stage-game environment, the first-best cannot be implemented as a perfect public equilibrium (PPE) of the infinitely repeated game either. Instead, at any constrained efficient PPE, the active agent "shirks" infinitely often, and when crisis happens, the active agent is "bailed out" infinitely often. The frequencies of crisis and bailout are endogenously determined in equilibrium. The welfare optimal equilibrium being characterized by recurrent crises and bailouts is consistent with historical episodes of financial crises, which features varying frequency and varied external responses for troubled institutions and countries in the real world. We explore some comparative statics of the PPEs of the repeated game numerically. |
| Keywords: | Bailouts; Moral Hazard; Repeated Games; Imperfect monitoring; Second best |
| JEL: | C73 D82 |
| Date: | 2022–01–05 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedrwp:93835&r= |
| By: | Zsombor Z. M\'eder; Carsten K. W. de Dreu; J\"org Gross |
| Abstract: | Attempts at predatory capture may provoke a defensive response that reduces the very value of the predated resource. We provide a game-theoretic analysis of simultaneous-move, two-player Attacker-Defender games that model such interactions. When initial endowments are equal, Attackers win about a third of such games in equilibrium. Under power disparities, Attackers become particularly aggressive when they are approximately one-third poorer than Defenders. With non-conflictual outside options Attackers become exceptionally aggressive when their opponent has access to high-benefit, low-cost production, and refrain from attack most when they are unilaterally provided with a high-benefit, high-cost production option. |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2202.10072&r= |
| By: | Maria Montero (School of Economics, University of Nottingham); Alex Possajennikov (School of Economics, University of Nottingham) |
| Abstract: | This paper studies a simple process of demand adjustment in cooperative games. In the process, a randomly chosen player makes the highest possible demand subject to the demands of other coalition members being satisfied. This process converges to the aspiration set; in convex games, this implies convergence to the core. We further introduce perturbations into the process, where players sometimes make a higher demand than feasible. These perturbations make the set of separating aspirations, i.e., demand vectors in which no player is indispensable in order for other players to achieve their demands, the one most resistant to mutations. We fully analyze this process for 3-player games. We further look at weighted majority games with two types of players. In these games, if the coalition of all small players is winning, the process converges to the unique separating aspiration; otherwise, there are many separating aspirations and the process reaches a neighbourhood of a separating aspiration. |
| Keywords: | demand adjustment, aspirations, core, stochastic stability |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:not:notcdx:2022-05&r= |
| By: | Xiaoliang Li |
| Abstract: | In this discussion draft, we investigate five different models of duopoly games, where the market is assumed to have an isoelastic demand function. Moreover, quadratic cost functions reflecting decreasing returns to scale are considered. The games in this draft are formulated with systems of two nonlinear difference equations. Existing equilibria and their local stability are analyzed by symbolic computations. In the model where a gradiently adjusting player and a rational (or a boundedly rational) player compete with each other, diseconomies of scale are proved to have an effect of stability enhancement, which is consistent with the similar results found by Fisher for homogeneous oligopolies with linear demand functions. |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2203.09972&r= |
| By: | Rahul Chandan (University of California, Santa Barbara); Keith Paarporn (University of California, Santa Barbara); Dan Kovenock (Economic Science Institute, Chapman University); Mahnoosh Alizadeh (University of California, Santa Barbara); Jason R. Marden (University of California, Santa Barbara) |
| Abstract: | Success in adversarial environments often requires investment into additional resources in order to improve one’s competitive position. But, can intentionally decreasing one’s own competitiveness ever provide strategic benefits in such settings? In this paper, we focus on characterizing the role of “concessions†as a component of strategic decision making. Specifically, we investigate whether a player can gain an advantage by either conceding budgetary resources or conceding valuable prizes to an opponent. While one might na¨ıvely assume that the player cannot, our work demonstrates that – perhaps surprisingly – concessions do offer strategic benefits when made correctly. In the context of General Lotto games, we first show that neither budgetary concessions nor value concessions can be advantageous to either player in a 1-vs.-1 scenario. However, in settings where two players compete against a common adversary, we find opportunities for one of the two players to improve her payoff by conceding a prize to the adversary. We provide a set of sufficient conditions under which such concessions exist. |
| Keywords: | General Lotto; Colonel Blotto; game; system security; defense; strategic pre-commitment; concession |
| JEL: | C72 D74 H56 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:21-24&r= |
| By: | John Duffy (Department of Economics, University of California, Irvine, California, 92697); Seung Han Yoo (Department of Economics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul, Republic of Korea, 02841) |
| Abstract: | We provide a model of group sorting or polarization based on group identity alone. In our model, agents differ from one another in terms of a binary group identity. Groups may also differ in terms of the distribution of abilities, but the distribution of abilities by group is uncertain and both groups are ex-ante equally likely to be distributed in the same way. Each agent's ability is private information, but group identity is publicly observable. Young agents make a decision as to which of two locations they will reside in when old and play a stage game with others when they are old, based on their private histories from a previous stage game played in the location where they were born (and young). We show that, in equilibrium, agents endogenously sort themselves according to their group identity to two different locations under rational belief updating, and we identify conditions under which the society becomes completely polarized with members of each group rationally choosing to congregate in distinct locations. |
| Keywords: | Polarization, group bias, homophily, private monitoring, sorting, Bayesian learning. |
| JEL: | C72 C73 D83 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:iek:wpaper:2202&r= |
| By: | Keith Paarporn (Department of Electrical and Computer Engineering, University of California, Santa Barbara); Rahul Chandan (Department of Electrical and Computer Engineering, University of California, Santa Barbara); Dan Kovenock (Economic Science Institute, Argyros School of Business and Economics at Chapman University); Mahnoosh Alizadeh (Department of Electrical and Computer Engineering, University of California, Santa Barbara); Jason R. Marden (Department of Electrical and Computer Engineering, University of California, Santa Barbara) |
| Abstract: | Strategic decision-making in uncertain and adversarial environments is crucial for the security of modern systems and infrastructures. A salient feature of many optimal decision-making policies is a level of unpredictability, or randomness, which helps to keep an adversary uncertain about the system’s behavior. This paper seeks to explore decision-making policies on the other end of the spectrum – namely, whether there are benefits in revealing one’s strategic intentions to an opponent before engaging in competition.We study these scenarios in a well-studied model of competitive resource allocation problem known as General Lotto games. In the classic formulation, two competing players simultaneously allocate their assets to a set of battlefields, and the resulting payoffs are derived in a zero-sum fashion. Here, we consider a multi-step extension where one of the players has the option to publicly pre-commit assets in a binding fashion to battlefields before play begins. In response, the opponent decides which of these battlefields to secure (or abandon) by matching the pre-commitment with its own assets. They then engage in a General Lotto game over the remaining set of battlefields. Interestingly, this paper highlights many scenarios where strategically revealing intentions can actually significantly improve one’s payoff. This runs contrary to the conventional wisdom that randomness should be a central component of decision-making in adversarial environments. |
| Keywords: | General Lotto; Colonel Blotto; game; system security; defense; strategic pre-commitment |
| JEL: | C72 D74 H56 |
| Date: | 2021 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:21-23&r= |
| By: | Haucap, Justus; Heldman, Christina; Rau, Holger A. |
| Abstract: | Many cartels are formed by individual managers of different firms, but not by firms as collectives. However, most of the literature in industrial economics neglects individuals' incentives to form cartels. Although oligopoly experiments reveal important insights on individuals acting as firms, they largely ignore individual heterogeneity, such as gender differences. We experimentally analyze gender differences in prisoner's dilemmas, where collusive behavior harms a passive third party. In a control treatment, no externality exists. To study the influence of social distance, we compare subjects' collusive behavior in a within-subjects setting. In the first game, subjects have no information on other players, whereas they are informed about personal characteristics in the second game. Results show that guilt-averse women are significantly less inclined to collude than men when collusion harms a third party. No gender difference can be found in the absence of a negative externality. Interestingly, we find that women are not sensitive to the decision context, i.e., even when social distance is small they hardly behave collusively when collusion harms a third party. |
| Keywords: | Collusion,Cartels,Competition Policy,Antitrust,Gender Differences |
| JEL: | C92 D01 D43 J16 K21 L13 L41 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:dicedp:380&r= |
| By: | Takashi Ui (Hitotsubashi University) |
| Abstract: | A policymaker discloses public information to interacting agents who also acquire costly private information. More precise public information reduces the precision and cost of acquired private information. Considering this effect, what disclosure rule should the policymaker adopt? We address this question under two alternative assumptions using a linear quadratic Gaussian game with arbitrary quadratic material welfare and convex information costs. First, the policymaker knows the cost of private information and adopts an optimal disclosure rule to maximize the expected welfare. Second, the policymaker is uncertain about the cost and adopts a robust disclosure rule to maximize the worst-case welfare. Depending on the elasticity of marginal cost, an optimal rule is qualitatively the same as that in the case of either a linear information cost or exogenous private information. Full disclosure is robust if and only if it is optimal under some information costs, even when no disclosure is optimal under other information costs. |
| Keywords: | public information; private information; crowding-out effect; linear quadratic Gaussian game; optimal disclosure; robust disclosure; information cost. |
| JEL: | C72 D82 E10 |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:upd:utmpwp:039&r= |
| By: | Pierre-Richard Agénor; Timothy Jackson; Luiz Awazu Pereira da Silva |
| Abstract: | A core-periphery model with financial frictions, imperfect financial integration, and cross-border banking is used to assess the magnitude of regulatory spillovers and the gains from international macroprudential policy coordination. A core global bank lends to its affiliates in the periphery and banks in both regions are subject to risk-sensitive capital regulation. Following an expansionary monetary policy in the core, a countercyclical response in capital requirements induces the global bank to engage in regulatory arbitrage. The magnitude of the resulting cross-border capital flows depends on the degree of economies of scope in lending. Welfare gains associated with countercyclical capital buffers are calculated for three policy regimes: independent policies (Nash), coordination, and reciprocity---a regime in which capital ratios set in the core are imposed on branches operating in the periphery. If regulators set policies on the basis of a narrow financial stability mandate, and these policies are evaluated in terms of household welfare, reciprocity may perform better than Nash, and as well as coordination for all parties, when regulatory leakages are strong. |
| Keywords: | global banking, financial spillovers, regulatory leakages, macroprudential policy coordination. |
| JEL: | E58 F42 F62 |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:bis:biswps:1007&r= |
| By: | Piolatto, A. (Tilburg University, Center For Economic Research); Schuett, Florian (Tilburg University, Center For Economic Research) |
| Keywords: | anonymous information platforms; opaque products; horizontal competition; experience goods; mismatch costs |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiucen:ac184e2f-0492-4738-b455-82a1385114f6&r= |
| By: | Lawrence Christiano; Husnu Dalgic; Xiaoming Li |
| Abstract: | Our primary finding is that surprisingly small changes in assumptions which determine the amount of net worth available in a bank panic have an important impact on the nature of the equilibria: there may not be a bank panic at all, or there may be several di erent panics of di erent severity. The economic reasons for this sensitivity are clarified by transforming the market economy into a game and studying banker best response functions. To establish robustness to model details, we report similar quantitative results across three di erent model specifications and calibrations. A second, additional result, is displayed in a three-period version of the panic model of Gertler and Kiyotaki (2015). That model naturally suggests the idea that welfare can be improved by imposing a restriction on bank leverage. We compute the Ramsey-optimal leverage restriction, but find that there is an implementation problem: the restriction can be associated with more than one equilibrium, not just the desired one. We discuss one way to address the implementation problem. |
| Keywords: | Bank runs, financial crises, macroprudential policy |
| JEL: | E44 G01 G21 |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2022_343&r= |