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on Game Theory |
| By: | Tom Johnston; Michael Savery; Alex Scott; Bassel Tarbush |
| Abstract: | We analyse the typical structure of games in terms of the connectivity properties of their best-response graphs. In particular, we show that almost every 'large' generic game that has a pure Nash equilibrium is connected, meaning that every non-equilibrium action profile can reach every pure Nash equilibrium via best-response paths. This has implications for dynamics in games: many adaptive dynamics, such as the best-response dynamic with inertia, lead to equilibrium in connected games. It follows that there are simple, uncoupled, adaptive dynamics for which period-by-period play converges almost surely to a pure Nash equilibrium in almost every 'large' generic game that has one. We build on recent results in probabilistic combinatorics for our characterisation of game connectivity. |
| Date: | 2023–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2309.10609&r=gth |
| By: | Bertrand Crettez (Université Paris-Panthéon-Assas, CRED - Centre de Recherche en Economie et Droit - Université Paris-Panthéon-Assas); Rabia Nessah (IESEG - UCL - Université catholique de Lille, LEM - Laboratoire d'Economie et de Management - UNS - Université Nice Sophia Antipolis (1965 - 2019) - CNRS - Centre National de la Recherche Scientifique - UCA - Université Côte d'Azur); Tarik Tazdaït (CNRS - Centre National de la Recherche Scientifique, CIRED - Centre International de Recherche sur l'Environnement et le Développement - Cirad - Centre de Coopération Internationale en Recherche Agronomique pour le Développement - EHESS - École des hautes études en sciences sociales - AgroParisTech - ENPC - École des Ponts ParisTech - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique, EHESS - École des hautes études en sciences sociales) |
| Abstract: | We propose a new notion of coalitional equilibria, the strong β-hybrid solution, which is a refinement of the hybrid solution introduced by Zhao. Zhao's solution is well suited to study situations where people cooperate within coalitions but where coalitions compete with one another. This paper's solution, as opposed to the hybrid solution, assigns to each coalition a strategy profile that is strongly Pareto optimal. Moreover, like the β-core, deviations by subcoalitions of any existing coalition are deterred by the threat of a unique counter-strategy available to the non-deviating players. Zhao proved the existence of existence of strong β-hybrid solution for transferable utility games with compact and convex strategy spaces and concave continuous payoff functions. Here, we extend his result to non-transferable utility games. |
| Keywords: | α-core β-core N -person game coalition structure hybrid solution strong hybrid solution, α-core, β-core, N -person game, coalition structure, hybrid solution, strong hybrid solution |
| Date: | 2023–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-04204632&r=gth |
| By: | Puru Gupta; Saul D. Jacka |
| Abstract: | We consider an augmented version of Merton's portfolio choice problem, where trading by large investors influences the price of underlying financial asset leading to strategic interaction among investors, with investors deciding their trading rates independently and simultaneously at each instant, in the spirit of dynamic Cournot competition, modelled here as a non-zero sum singular stochastic differential game. We establish an equivalence result for the value functions of an investor's best-response problem, which is a singular stochastic optimal control problem, and an auxiliary classical stochastic optimal control problem by exploiting the invariance of the value functions with respect to a diffeomorphic integral flow associated with the drift coefficient of the best-response problem. Under certain regularity conditions, we show that the optimal trajectories of the two control problems coincide, which permits analytical characterization of Markov-Nash equilibrium portfolios. For the special case when asset price volatility is constant, we show that the unique Nash equilibrium is deterministic, and provide a closed-form solution which illuminates the role of imperfect competition in explaining the excessive trade puzzle. |
| Date: | 2023–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2309.16047&r=gth |
| By: | Effrosyni Diamantoudi (Concordia University Montreal); Eftichios S. Sartzetakis (Department of Economics, University of Macedonia); Stefania Strantza (Thompson Rivers University) |
| Abstract: | The paper provides a fresh look at the literature on the formation of international environmental agreements by introducing into the classic model emissions and abatement as countries’ separate choice variables. The model’s structure is kept unchanged, assuming a two-stage game in which the internal and external stability conditions define coalition’s stability. We illustrate the way in which each of the three components of countries welfare, benefits from own emissions, damages from aggregate emissions and own abatement costs, interact in determining nonsignatories’ equilibrium choices, which in turn, determine the stable coalition’s size. We show that, ceteris paribus, as abatement becomes cheaper, nonsignatories become more responsive to signatories’ choices, strengthening the signatories’ leadership position, allowing thus, largest stable coalitions to be formed. However, when abatement costs are low the same choices are individually rational, that is, forming a coalition does not add much over the Nash. Furthermore, large stable coalitions are possible under high abatement costs, only if damages are high relative to benefits, but such coalitions require negative net emissions. Finally, in the absence of leadership, only very small coalitions are stable. Therefore, even if the coalition has leadership power in setting abatement and emission targets, the reduction of free-riding incentives is significant, yielding larger stable coalitions, only when it is welfare irrelevant, i.e., when the same targets are individually rational. |
| Keywords: | Coalition Formation, International Environmental Agreements, Size of Stable Coalitions |
| JEL: | D6 Q5 C7 |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:mcd:mcddps:2023_04&r=gth |
| By: | Shoji Haruna; Rajeev K. Goel |
| Abstract: | This paper adds to the literature on transboundary pollution by considering pollution related to both production and consumption activities. In particular, we consider a symmetric strategic two firm-two country game model with bilateral trade and transboundary pollution to analyze the effects of trade liberalization on economic performance under two types of pollution. Our game-theoretic results with two trading countries find significant differences compared to the case where only production pollution is considered. When trade liberalization policy is mutually implemented, consumer surplus and social environmental damage in the Home and Foreign countries are both increased under production pollution, while they are both decreased under consumption pollution. Furthermore, when the two countries face either production or consumption pollution composed of transboundary pollution and local pollution, consumer surplus, producer surplus, and social environmental damage are larger in the presence of consumption pollution than in the presence of production pollution; and, under certain conditions, social welfare can be larger or smaller in the presence of production pollution than in the presence of consumption pollution. It is uniquely shown that in the three-stage game model trade policy may lose its effectiveness as a policy under consumption pollution. Policy implications are discussed. |
| Keywords: | environment, transboundary pollution, consumption pollution, production pollution, trade liberalization, environment tax, oligopoly, tariff |
| JEL: | D43 F13 L13 Q56 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10667&r=gth |
| By: | Ahmed, Rafayal; Shopp, Colin |
| Abstract: | We analyze firms’ incentives to acquire information about market demand in a differentiated goods duopoly setting. We find two distinct benefits of having better information. Firstly, with better information, each firm can better match its price to demand. This benefit is decreasing in the level of market competition. Secondly, better information allows each firm to coordinate their prices with each other in different states, and each firm can make better use of its own information if the other firm acquires better information. This benefit is inverse u-shaped in the level of competition. Based on which effect dominates, each firm’s total benefit from information can either be decreasing, or inverse u-shaped in the level of competition. Given endogenous information acquisition decisions by firms, the effect of competition on consumer welfare is ambiguous. |
| Keywords: | Information acquisition, Bertrand duopoly, signals, competition. |
| JEL: | D43 D81 D84 L13 |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:118311&r=gth |
| By: | Susanne Goldluecke; Thomas Troeger |
| Abstract: | We present a class of simple transfer-free rules that are very effective tools for assigning an unpleasant task among a group of agents: agents decide simultaneously whether or not to “volunteer”; if the number of volunteers exceeds a threshold number, the task is assigned to a volunteer; if the number is below the threshold, the task is assigned to a non-volunteer. In a setting in which agents have non-trivial preferences over who performs the task, such a threshold rule is utilitarian optimal across all binary-action rules. In a large group, the first best is reached approximately via a threshold rule with a large threshold. Threshold rules have a robust-improvement property: any rule with a non-extreme threshold always has an equilibrium that yields a strict interim Pareto improvement over a random task assignment. We show that assigning the task to a non-volunteer rather than randomly among all agents if the threshold is not reached is crucial for this result. Such a uniformly-random default, however, is utilitarian optimal if ex-post participation constraints are imposed, and is still good enough to approximate the first best in a large population. The results can be adapted to the problem of assigning a pleasant task. |
| Keywords: | volunteers’ dilemma, mechanism design without transfers, binary-action mechanism |
| JEL: | H41 D82 |
| Date: | 2023–09 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2023_464&r=gth |
| By: | Georgios Petropoulos; Bertin Martens; Geoffrey Parker; Marshall Van Alstyne |
| Abstract: | Digital platforms, empowered by artificial intelligence algorithms, facilitate efficient interactions between consumers and merchants that allow the collection of profiling information which drives innovation and welfare. Private incentives, however, lead to information asymmetries resulting in market failures. This paper develops a product differentiation model of competition between two platforms to study private and social incentives to share information. Sharing information can be welfare-enhancing because it solves the data bottleneck market failure. Our findings imply that there is scope for the introduction of a mandatory information sharing mechanism from big tech to their competitors that help the latter to improve their network value proposition and become more competitive in the market. The price of information in this sharing mechanism matters. We show that price regulation over information sharing like the one applied in the EU jurisdiction increases the incentives of big platforms to collect and analyze more data. It has ambiguous effects on their competitors that depend on the exact relationship between information and network value. |
| Keywords: | information sharing, digital platforms, data bottleneck, data portability |
| JEL: | D47 D82 K21 L21 L22 L40 L41 L43 L51 L86 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10663&r=gth |
| By: | Jacopo Gambato; Martin Peitz |
| Abstract: | We analyze consumers’ voluntary information disclosure in a platform setting. For given consumer participation, the platform and sellers tend to prefer limited disclosure of consumer valuations, in contrast to consumers. With endogenous consumer participation, seller and platform incentives may be misaligned, and sellers may be better off when consumers can disclose their valuations. A regulator acting in the best interest of consumers and/or sellers may want to intervene and force the platform to employ a disclosure technology that enables consumers to voluntarily disclose information from a richer message space. |
| Keywords: | Two-sided platform, platform governance, information disclosure, information design, privacy regulation, e-commerc |
| JEL: | L12 L15 D21 D42 M37 |
| Date: | 2023–09 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2023_468&r=gth |
| By: | Peña, Jorge; Mullon, Charles; Lehmann, Laurent |
| Abstract: | Many social interactions happen indirectly via modifications of environmental variables, e.g. through the depletion of renewable resources or the secretion of functional compounds. Here, we derive the selection gradient on a quantitative trait affecting the dynamics of such environmental vari-ables that feedback on reproduction and survival in a patch-structured population that is finite, of con-stant size, and subject to isolation by distance. Our analysis shows that the selection gradient depends on how a focal individual influences the fitness of all future individuals in the population through modifications of the environmental variables they experience, weighted by the neutral relatedness be-tween recipients and the focal. The evolutionarily relevant trait-driven environmental modifications are formalized as the extended phenotypic effects of an individual, which quantify how a trait change in the individual in the present affects the environmental variables in all patches at all future times. When the trait affects reproduction and survival through some payoff function, the selection gradient can be expressed in terms of extended phenotypic effects weighted by scaled-relatedness coefficients. We show how to compute extended phenotypic effects, relatedness, and scaled-relatedness coefficients using Fourier analysis, allowing us to investigate a broad class of environmentally mediated social in-teractions in a tractable way. We illustrate our approach by studying the evolution of a trait controlling the costly production of some lasting commons (e.g. a common-pool resource or a toxic compound) that can diffuse in space. We show that whether selection favours environmentally mediated altruism or spite depends on the spatial correlation between an individual’s lineage and the commons originat-ing from its patch. The sign of this correlation depends on interactions between dispersal patterns and the commons’ renewal dynamics. More broadly, we suggest that selection can favour a wide range of social behaviours when these are mediated in space and time through environmental feedback. |
| Keywords: | Adaptive dynamics; Metacommunity; Extended Phenotype; Altruism; Spite |
| Date: | 2023–10–02 |
| URL: | http://d.repec.org/n?u=RePEc:tse:iastwp:128557&r=gth |
| By: | Daniela Del Boca; Christopher Flinn; Ewout Verriest; Matthew Wiswall |
| Abstract: | We construct a dynamic model of child development where forward-looking parents and children jointly take actions to increase the child’s cognitive and non-cognitive skills within a Markov Perfect Equilibrium framework. In addition to time and money investments in their child, parents also choose whether to use explicit incentives to increase the child’s self-investment, which may reduce the child’s future intrinsic motivation to invest by reducing the child’s discount factor. We use the estimated model parameters to show that the use of extrinsic motivation has large costs in terms of the child’s future incentives to invest in themselves. |
| Keywords: | time allocation, child development, parenting styles |
| JEL: | J13 D10 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10641&r=gth |
| By: | Chrysovalantou Milliou |
| Abstract: | This paper explores why competing firms can choose to outsource to an external common supplier that does not have a cost advantage in input production. The supplier, through its contract offers, manages to generate asymmetry, to alter product market competition, and to extract profits from the competing .rms. Two-part tariffs and sequential contracting are both crucial for the emergence of outsourcing. The supplier purposefully avoids industry pro.t maximization to enlarge its profits share. Both consumer and total welfare benefit from the presence of an otherwise redundant supplier in the market. |
| Keywords: | outsourcing, strategic outsourcing, make-or-buy, two-part tariffs, common supplier, sequential contracting |
| JEL: | D43 L11 L22 L23 L24 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10645&r=gth |