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on Game Theory |
| By: | Andrea Bovo; Tiziano De Angelis; Jan Palczewski |
| Abstract: | We study zero-sum stochastic games between a singular controller and a stopper when the (state-dependent) diffusion matrix of the underlying controlled diffusion process is degenerate. In particular, we show the existence of a value for the game and determine an optimal strategy for the stopper. The degeneracy of the dynamics prevents the use of analytical methods based on solution in Sobolev spaces of suitable variational problems. Therefore we adopt a probabilistic approach based on a perturbation of the underlying diffusion modulated by a parameter $\gamma>0$. For each $\gamma>0$ the approximating game is non-degenerate and admits a value $u^\gamma$ and an optimal strategy $\tau^\gamma_*$ for the stopper. Letting $\gamma\to 0$ we prove convergence of $u^\gamma$ to a function $v$, which identifies the value of the original game. We also construct explicitly optimal stopping times $\theta^\gamma_*$ for $u^\gamma$, related but not equal to $\tau^\gamma_*$, which converge almost surely to an optimal stopping time $\theta_*$ for the game with degenerate dynamics. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.00613&r=gth |
| By: | Léa Munich (Université de Franche-Comté, CRESE, F-25000 Besançon, France) |
| Abstract: | In this paper, we optimize and allocate the costs of a non-rival common-pool resource among several users. In such a so-called schedule situation the players have different demands given by distinct subsets of periods satisfying their needs. The total costs resulting from shared use of the resource are allocated by natural allocations called Equal Pooling allocations, in which the cost of each needed period is shared equally among the users of this period. The associated schedule game gives, for each coalition of players, the minimal cost of a period configuration satisfying the needs of all its members. We have three main contributions. First, we provide several sufficient conditions for the non-emptiness of the core of a schedule game. Second, we prove that under some of these conditions the Shapley value is in the core and coincides with some Equal pooling allocation. Third, we establish connections with other classes of operational research games. Furthermore, we present an application to the allocation of the common costs of the mail carrier route of La Poste, the french postal operator. |
| Keywords: | Game theory, Schedule, OR-game, Cost allocation, Equal pooling allocations |
| JEL: | C71 L87 |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:crb:wpaper:2023-08&r=gth |
| By: | Eric Gao; Daniel Luo |
| Abstract: | How does receiver commitment affect incentives for information revelation in Bayesian persuasion? We study many-sender persuasion games where a single receiver commits to a posterior-dependent action profile, or allocation, before senders design the informational environment. We develop a novel revelation-like principle for ex-ante mechanism design settings where sender reports are Blackwell experiments and use it to characterize the set of implementable allocations in our model. We show global incentive constraints are pinned down by ``worst-case'' punishments at finitely many posterior beliefs, whose values are independent of the allocation. Moreover, the receiver will generically benefit from the ability to randomize over deterministic outcomes when solving for the constrained optimal allocation, in contrast to standard mechanism design models. Finally, we apply our results to analyze efficiency in multi-good allocation problems, full surplus extraction in auctions with allocation externalities, and optimal audit design, highlighting the role that monotone mechanisms play in these settings. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.02465&r=gth |
| By: | Yu-Jui Huang; Li-Hsien Sun |
| Abstract: | This paper considers finitely many investors who perform mean-variance portfolio selection under a relative performance criterion. That is, each investor is concerned about not only her terminal wealth, but how it compares to the average terminal wealth of all investors (i.e., the mean field). At the inter-personal level, each investor selects a trading strategy in response to others' strategies (which affect the mean field). The selected strategy additionally needs to yield an equilibrium intra-personally, so as to resolve time inconsistency among the investor's current and future selves (triggered by the mean-variance objective). A Nash equilibrium we look for is thus a tuple of trading strategies under which every investor achieves her intra-personal equilibrium simultaneously. We derive such a Nash equilibrium explicitly in the idealized case of full information (i.e., the dynamics of the underlying stock is perfectly known), and semi-explicitly in the realistic case of partial information (i.e., the stock evolution is observed, but the expected return of the stock is not precisely known). The formula under partial information involves an additional state process that serves to filter the true state of the expected return. Its effect on trading is captured by two degenerate Cauchy problems, one of which depends on the other, whose solutions are constructed by elliptic regularization and a stability analysis of the state process. Our results indicate that partial information alone can reduce investors' wealth significantly, thereby causing or aggravating systemic risk. Intriguingly, in two different scenarios of the expected return (i.e., it is constant or alternating between two values), our Nash equilibrium formula spells out two distinct manners systemic risk materializes. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.04045&r=gth |
| By: | Christoph K\"uhn; Christopher Lorenz |
| Abstract: | We present a discrete time version of Kyle's (1985) classic model of insider trading. The model has three kinds of traders: an insider, random noise traders, and a market maker. The insider aims to exploit her informational advantage and maximise expected profits while the market maker observes the total order flow and sets prices accordingly. First, we show how the multi-period model with finitely many pure strategies can be reduced to a (static) social system in the sense of Debreu (1952) and prove the existence of a sequential Kyle equilibrium, following Kreps and Wilson (1982). This requires no probabilistic restrictions on the true value, the insider's dynamic information, and the noise trader's actions. In the single-period model we establish bounds for the insider's strategy in equilibrium. Finally, we prove the existence of an equilibrium for the game with a continuum of actions, by considering an approximating sequence of games with finitely many actions. Because of the lack of compactness of the set of measurable price functions, standard infinite-dimensional fixed point theorems are not applicable. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.00904&r=gth |
| By: | Francesco Fallucchi (Department of Economics, University of Bergamo); Francesco Trevisan (Department of Economics, Ca' Foscari University of Venice) |
| Abstract: | We study the Tullock contest model with desert concerns (Gill and Stone (2010)). In a contest with n possibly heterogeneous players and convex effort costs, we establish the conditions necessary for a unique Nash equilibrium in pure strategies. Subsequently, we analyze the impact of desert concerns on players' spending behavior, probability of winning, and rent dissipation. |
| Keywords: | rent-seeking, contest, asymmetry, desire to win, loss aversion |
| JEL: | D31 D72 D91 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:2023:31&r=gth |
| By: | Dylan Laplace Mermoud (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique); Michel Grabisch (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique); Peter Sudhölter (SDU - University of Southern Denmark) |
| Abstract: | Minimal balanced collections are a generalization of partitions of a finite set of n elements and have important applications in cooperative game theory and discrete mathematics. However, their number is not known beyond n = 4. In this paper we investigate the problem of generating minimal balanced collections and implement the Peleg algorithm, permitting to generate all minimal balanced collections till n = 7. Secondly, we provide practical algorithms to check many properties of coalitions and games, based on minimal balanced collections, in a way which is faster than linear programming-based methods. In particular, we construct an algorithm to check if the core of a cooperative game is a stable set in the sense of von Neumann and Morgenstern. The algorithm implements a theorem according to which the core is a stable set if and only if a certain nested balancedness condition is valid. The second level of this condition requires generalizing the notion of balanced collection to balanced sets. |
| Keywords: | minimal balanced collection, cooperative game, core, stable set, balancedness, hypergraph, algorithm |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-04356803&r=gth |
| By: | Bogliacino, Francesco (Universidad Nacional de Colombia); Aycinena, Diego (Universidad del Rosario); Kimbrough, Erik |
| Abstract: | We analyze and compare three methods of measuring norms: the Krupka and Weber (KW) coordination game, the two-step approach by Bicchieri and Xiao (BX), and a novel Binarized Scoring Method (BSM) we introduce that elicits the full distribution of normative beliefs. We test their effectiveness in two distinctive ways. First, we compare the fit and predictive power of the norms elicited by each method in 3 versions of the dictator game, which differ in how the pie is initially allocated. Then we use vignettes to assess the extent to which the methods can recover existing norms for various naturally occurring settings. We find that the KW method yields better predictive power within a norm-dependent utility model. All 3 methods effectively recover norms in field settings, although KW is more robust to false positives. |
| Date: | 2023–12–15 |
| URL: | http://d.repec.org/n?u=RePEc:osf:socarx:djfw5&r=gth |
| By: | Yongyang Cai; Khyati Malik; Hyeseon Shin |
| Abstract: | We build a dynamic multi-region model of climate and economy with emission permit trading among 12 aggregated regions in the world. We solve for the dynamic Nash equilibrium under noncooperation, wherein each region adheres to the emission cap constraints following commitments outlined in the 2015 Paris Agreement. Our model shows that the emission permit price reaches $749 per ton of carbon by 2050. We demonstrate that a regional carbon tax is complementary to the global cap-and-trade system, and the optimal regional carbon tax is equal to the difference between the regional marginal abatement cost and the permit price. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.15563&r=gth |
| By: | Guilherme Pelegrina (UNICAMP - Universidade Estadual de Campinas = University of Campinas); Leonardo Duarte (UNICAMP - Universidade Estadual de Campinas = University of Campinas); Michel Grabisch (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | Several practical applications can be formulated as a problem of estimating a source of interest from a set of mixed data collected by different sensors. Although a lot of effort has been done to address the optimization task in signal extraction, there is a lack in the literature on how to evaluate the contribution of each sensor in the extraction process. In this letter, we propose a model-agnostic approach that can be used to interpret both the contribution of each sensor in the estimated source and the interaction effects between them. Our proposal is based on a solution concept from game theory, called Shapley value. Numerical experiments on synthetic and real data attest the use of our proposal in blind source extraction problems. |
| Keywords: | signal extraction, sensors design, Shapley value |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-04356790&r=gth |
| By: | Patrick Allmis; Luca Paolo Merlino |
| Abstract: | In this paper, players contribute to two local public goods for which they have different tastes and sponsor costly links to enjoy the provision of others. In equilibrium, either there are several contributors specialized in public good provision or only two contributors who are not entirely specialized. Higher linking costs have a non-monotonic impact on welfare and polarization, as they affect who specializes in public good provision. When the available budget is small, subsidies should be given to players who already specialize in public good provision; otherwise, they should target only one player who specializes in public good provision. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.00457&r=gth |
| By: | Oren Ben-Zwi; Ilan Newman |
| Abstract: | We show that no efficient ascending auction can guarantee to find even a minimal envy-free price vector if all valuations are submodular, assuming a basic complexity theory's assumption. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.00522&r=gth |
| By: | Renato Soeiro; Alberto Pinto |
| Abstract: | We discuss price competition when positive network effects are the only other factor in consumption choices. We show that partitioning consumers into two groups creates a rich enough interaction structure to induce negative marginal demand and produce pure price equilibria where both firms profit. The crucial condition is one group has centripetal influence while the other has centrifugal influence. The result is contrary to when positive network effects depend on a single aggregate variable and challenges the prevalent assumption that demand must be micro-founded on a distribution of consumer characteristics with specific properties, highlighting the importance of interaction structures in shaping market outcomes. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.02865&r=gth |
| By: | Gonzo Damian Antonio |
| Abstract: | Anger is a negative emotion commonly experienced by all human beings, and it has proven effects on human cognition. Research in this field has shown that cognitive abilities diminish in angry individuals, a phenomenon referred to as "the depth of thought effect." This paper establishes a causal relationship between anger and the strategic sophistication of subjects in a laboratory setting. The experimental design involves an emotion-induction treatment and a beauty contest to measure the strategic sophistication of participants. Treated subjects report higher levels of anger and choose significantly higher numbers in the game, indicating a negative effect of anger on strategic sophistication. |
| JEL: | D1 |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:aep:anales:4658&r=gth |
| By: | Vincent Anesi; Peter Buisseret |
| Abstract: | We develop a dynamic model in which a group collectively bargains with an external party. At each date the group makes an offer to the external party (the ‘agent’) in exchange for a concession. Group members hold heterogeneous preferences over agreements and are uncertain about the agent’s resolve. We show that all group members favor more aggressive proposals than they would if they were negotiating alone. By eliciting more information about the agent’s resolve, these offers reduce the group members’ uncertainty about the agent’s preferences and therefore reduce the group’s internal conflicts over its negotiating strategy. To mitigate the consequent risk that negotiations fail, decisive group members successively give up their influence over proposals: starting from any initially democratic decision process, the group eventually consolidates its entire negotiation authority into the hands of a single member. |
| Keywords: | adverse selection, collective choice, political economy, dictatorship, bargaining |
| JEL: | D02 D71 D78 D82 L22 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10823&r=gth |
| By: | Martimort, David; Sand-Zantman, Wilfried |
| Abstract: | We analyze the effect of media mergers in a model that stresses, on the one hand, the fact that media are two-sided platforms willing to attract advertisers and viewers and, on the other hand, that strong competitors have emerged to challenge traditional media on both sides. We show that a merger has two conflicting effects on traditional media’s incentives to invest in quality programs and to exploit their market power. When competition is primarily between traditional media, a Business-Stealing Effect dominates, and the merger is detrimental to advertisers and viewers. When the competition is mainly between the traditional media and their new competitors, an Ecosystem Effect dominates, and the merger benefits advertisers and viewers. We extend this setting to discuss the role of financial constraints that might limit investments in the quality of programs and show that the same effects are at play. |
| Keywords: | Media; competition; merger |
| JEL: | L82 L22 G34 |
| Date: | 2023–12–05 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:128764&r=gth |
| By: | Andrew R. Tilman; Robert G. Haight |
| Abstract: | The benefits of investments in sustainability are often public goods that accrue at broad scales and to many people. Urban forests exemplify this; trees supply ecosystem service benefits from local (in the case of shade) to global (in the case of carbon sequestration) scales. The complex mosaic of public and private ownership that typically defines an urban forest makes the public goods problem of investing in forest sustainability especially acute. This results in incentives for private tree owners to invest in tree care that typically fall short of those of a public forest manager aiming for the social optimum. The management of a forest pest, such as emerald ash borer, provides a salient focus area because pests threaten the provision of public goods from urban forests and pest management generates feedback that alters pest spread and shapes future risks. We study how managers can design policies to address forest pest outbreaks and achieve uniform management across a mosaic of ownership types. We develop a game theoretic model to derive optimal subsidies for the treatment of forests pests and evaluate the efficacy of these policies in mitigating the spread of forest pests with a dynamic epidemiological model. Our results suggest that a combination of optimal treatment subsidies for privately owned trees and targeted treatment of public trees can be far more effective at reducing pest-induced tree mortality than either approach in isolation. While we focus on the management of urban forests, designing programs that align private and public incentives for investment in public goods could advance sustainability in a wide range of systems. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.05403&r=gth |