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on Game Theory |
| By: | Sam Ganzfried |
| Abstract: | While Nash equilibrium has emerged as the central game-theoretic solution concept, many important games contain several Nash equilibria and we must determine how to select between them in order to create real strategic agents. Several Nash equilibrium refinement concepts have been proposed and studied for sequential imperfect-information games, the most prominent being trembling-hand perfect equilibrium, quasi-perfect equilibrium, and recently one-sided quasi-perfect equilibrium. These concepts are robust to certain arbitrarily small mistakes, and are guaranteed to always exist; however, we argue that neither of these is the correct concept for developing strong agents in sequential games of imperfect information. We define a new equilibrium refinement concept for extensive-form games called observable perfect equilibrium in which the solution is robust over trembles in publicly-observable action probabilities (not necessarily over all action probabilities that may not be observable by opposing players). Observable perfect equilibrium correctly captures the assumption that the opponent is playing as rationally as possible given mistakes that have been observed (while previous solution concepts do not). We prove that observable perfect equilibrium is always guaranteed to exist, and demonstrate that it leads to a different solution than the prior extensive-form refinements in no-limit poker. We expect observable perfect equilibrium to be a useful equilibrium refinement concept for modeling many important imperfect-information games of interest in artificial intelligence. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.16506&r=gth |
| By: | Tam\'as Solymosi |
| Abstract: | We characterize the assignment games which admit a population monotonic allocation scheme (PMAS) in terms of efficiently verifiable structural properties of the nonnegative matrix that induces the game. We prove that an assignment game is PMAS-admissible if and only if the positive elements of the underlying nonnegative matrix form orthogonal submatrices of three special types. In game theoretic terms it means that an assignment game is PMAS-admissible if and only if it contains a veto player or a dominant veto mixed pair or is composed of from these two types of special assignment games. We also show that in a PMAS-admissible assignment game all core allocations can be extended to a PMAS, and the nucleolus coincides with the tau-value. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.17373&r=gth |
| By: | Trivikram Dokka; Jorge Bruno; Sonali SenGupta; Chowdhury Mohammad Sakib Anwar |
| Abstract: | We study equilibria in an Electric Vehicle (EV) charging game, a cost minimization game inherent to decentralized charging control strategy for EV power demand management. In our model, each user optimizes its total cost which is sum of direct power cost and the indirect dissatisfaction cost. We show that, taking player specific price independent dissatisfaction cost in to account, contrary to popular belief, herding only happens at lower EV uptake. Moreover, this is true for both linear and logistic dissatisfaction functions. We study the question of existence of price profiles to induce a desired equilibrium. We define two types of equilibria, distributed and non-distributed equilibria, and show that under logistic dissatisfaction, only non-distributed equilibria are possible by feasibly setting prices. In linear case, both type of equilibria are possible but price discrimination is necessary to induce distributed equilibria. Finally, we show that in the case of symmetric EV users, mediation cannot improve upon Nash equilibria. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.15035&r=gth |
| By: | David Bartl; Mikl\'os Pint\'er |
| Abstract: | We consider transferable utility cooperative games with infinitely many players. In particular, we generalize the notions of core and balancedness, and also the Bondareva-Shapley Theorem for infinite TU-games with and without restricted cooperation, to the cases where the core consists of $\kappa$-additive set functions. Our generalized Bondareva-Shapley Theorem extends previous results by Bondareva (1963), Shapley (1967), Schmeidler (1967), Faigle (1989), Kannai (1969), Kannai (1992), Pinter(2011) and Bartl and Pint\'er (2022). |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.05843&r=gth |
| By: | Burton-Chellew, Maxwell; West, Stuart |
| Abstract: | The black box method was developed as an ‘asocial control’ to measure the potential role of payoff-based learning in social dilemmas [1]. Players must decide how many virtual coins they want to input into a virtual black box that will provide uncertain returns. But in truth, they are playing with each other in a repeated social game. By ‘black boxing’ the game’s social aspects and payoffs, the method creates a population of self-interested but ignorant or confused individuals that must learn the games payoffs. This provides a behaviourally measured null hypothesis for testing social behaviours, as opposed to the idealized and stringent predictions of rational self-interested agents (Homo economicus). However, a potential problem is that participants can unwittingly affect other participants. Here we test a solution to this problem, in a range of public goods games, by making participants interact, unknowingly, with simulated players (‘computerized black box’). We find no significant differences in rates of learning between the original and the computerized black box. These results, along with the fact that simulated agents can be programmed to behave in different ways, mean that the computerized black box has great potential for studying how individuals learn under different environments in social dilemmas. |
| Date: | 2022–09–29 |
| URL: | http://d.repec.org/n?u=RePEc:osf:socarx:5k4ez&r=gth |
| By: | Ryan Donnelly; Zi Li |
| Abstract: | Agents attempt to maximize expected profits earned by selling multiple units of a perishable product where their revenue streams are affected by the prices they quote as well as the distribution of other prices quoted in the market by other agents. We propose a model which captures this competitive effect and directly analyze the model in the mean-field limit as the number of agents is very large. We classify mean-field Nash equilibrium in terms of the solution to a Hamilton-Jacobi-Bellman equation and a consistency condition and use this to motivate an iterative numerical algorithm to compute equilibrium. Properties of the equilibrium pricing strategies and overall market dynamics are then investigated, in particular how they depend on the strength of the competitive interaction and the ability to oversell the product. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.17208&r=gth |
| By: | Benjamin Balzer; Antonio Rosato |
| Abstract: | We characterize optimal reserve prices in first-price and second-price auctions with independent private values when bidders are expectations-based loss averse. Under ``unacclimating personal equilibrium", the optimal public reserve price can be lower than under risk neutrality or risk aversion. Moreover, secret and random reserve prices raise more revenue than public ones since, by giving every bidder a chance to win, they expose all bidders to the ``attachment effect". In contrast, under ``choice-acclimating personal equilibrium", the optimal reserve price is public and differs across the two auction formats. Furthermore, the seller excludes more types compared to the risk-neutral and risk-averse benchmarks. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.10938&r=gth |
| By: | Zachary Fulker; Patrick Forber; Rory Smead; Christoph Riedl |
| Abstract: | Sending and receiving signals is ubiquitous in the living world. It includes everything from individual molecules triggering complex metabolic cascades, to animals using signals to alert their group to the presence of predators. When communication involves common interest, simple sender-receiver games show how reliable signaling can emerge and evolve to transmit information effectively. These games have been analyzed extensively, with some work investigating the role of static network structure on information transfer. However, no existing work has examined the coevolution of strategy and network structure in sender-receiver games. Here we show that coevolution is sufficient to generate the endogenous formation of distinct groups from an initially homogeneous population. It also allows for the emergence of novel ``hybrid'' signaling groups that have not previously been considered or demonstrated in theory or nature. Hybrid groups are composed of different complementary signaling behaviors that rely on evolved network structure to achieve effective communication. Without this structure, such groups would normally fail to effectively communicate. Our findings pertain to all common interest signaling games, are robust across many parameters, and mitigate known problems of inefficient communication. Our work generates new insights for the theory of adaptive behavior, signaling, and group formation in natural and social systems across a wide range of environments in which changing network structure is common. We discuss implications for research on metabolic networks, among neurons, proteins, and social organisms. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.17309&r=gth |
| By: | Marius Alt (European Commission’s Joint Research Centre, Ispra, Italy); Carlo Gallier (Free University of Bozen-Bolzano, Italy); Martin Kesternich (ZEW – Leibniz Centre for European Economic Research, the University of Kassel, Germany); Bodo Sturm (ZEW – Leibniz Centre for European Economic Research, Germany) |
| Abstract: | We experimentally test a theoretically promising amendment to the ratchet-up mechanism of the Paris Agreement. The ratchet-up mechanism prescribes that parties’ commitments to the global response to climate change cannot decrease over time and our results confirm that its effect is detrimental. We design a public goods game to study whether an amendment to the mechanism that stipulates all agents to contribute at least a collective minimum to the public good which is based on the principle of the lowest common denominator promotes cooperation. We find that binding collective minimum contributions improve the effectiveness of the ratchet-up mechanism. Non-binding minimum contributions, in contrast, do not foster cooperation. Our data reveal conditional cooperative dynamics to explain the difference. If other participants contribute less than the collective minimum contributions, even initially cooperative participants start to negatively reciprocate such a form of non-compliance by contributing less. |
| Keywords: | Islam, Gender Equality, Ramadan, Social Norms, Illegal Behavior. |
| JEL: | C72 C92 H41 |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:bzn:wpaper:bemps96&r=gth |
| By: | Saeed Hadikhanloo (Tweag I/O); Rida Laraki (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique); Panayotis Mertikopoulos (LIG - Laboratoire d'Informatique de Grenoble - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes); Sylvain Sorin (IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité) |
| Abstract: | We examine the long-run behavior of a wide range of dynamics for learning in nonatomic games, in both discrete and continuous time. The class of dynamics under consideration includes fictitious play and its regularized variants, the best reply dynamics (again, possibly regularized), as well as the dynamics of dual averaging / "follow the regularized leader" (which themselves include as special cases the replicator dynamics and Friedman's projection dynamics). Our analysis concerns both the actual trajectory of play and its time-average, and we cover potential and monotone games, as well as games with an evolutionarily stable state (global or otherwise). We focus exclusively on games with finite action spaces; nonatomic games with continuous action spaces are treated in detail in Part Ⅱ. |
| Date: | 2022–10–04 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03767995&r=gth |
| By: | Cabrales, Antonio; Hauk, Esther |
| Abstract: | In this paper we model the interaction between leaders, their followers and crowd followers in a coordination game with local interaction. The steady states of a dynamic best-response process can feature a coexistence of Pareto dominant and risk dominant actions in the population. The existence of leaders and their followers, plus the local interaction, which leads to clustering, is crucial for the survival of the Pareto dominant actions. The evolution of leader and crowd followership shows that leader followership can also be locally stable around Pareto dominant leaders. The paper answers the questions (i) which Leader should be removed and (ii) how to optimally place leaders in the network to enhance payoff dominant play. |
| Date: | 2022–07–12 |
| URL: | http://d.repec.org/n?u=RePEc:osf:socarx:8mect&r=gth |
| By: | Florian Brandl (HCM - Hausdorff Center for Mathematics - Rheinische Friedrich-Wilhelms-Universität Bonn); Felix Brandt (TUM - Technische Universität Munchen - Université Technique de Munich [Munich, Allemagne]); Matthias Greger (TUM - Technische Universität Munchen - Université Technique de Munich [Munich, Allemagne]); Dominik Peters (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique); Christian Stricker (TUM - Technische Universität Munchen - Université Technique de Munich [Munich, Allemagne]); Warut Suksompong (NUS - National University of Singapore) |
| Abstract: | We study a mechanism design problem where a community of agents wishes to fund public projects via voluntary monetary contributions by the community members. This serves as a model for public expenditure without an exogenously available budget, such as participatory budgeting or voluntary tax programs, as well as donor coordination when interpreting charities as public projects and donations as contributions. Our aim is to identify a mutually beneficial distribution of the individual contributions. In the preference aggregation problem that we study, agents with linear utility functions over projects report the amount of their contribution, and the mechanism determines a socially optimal distribution of the money. We identify a specific mechanism-the Nash product rule-which picks the distribution that maximizes the product of the agents' utilities. This rule is Pareto efficient and incentivizes agents to contribute their entire budget while spending each agent's contribution only on projects the agent finds acceptable. |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03818329&r=gth |
| By: | Schauf, Andrew; Oh, Poong |
| Abstract: | When populations share common-pool resources (CPRs), individuals decide how much effort to invest towards resource extraction and how to allocate this effort among available resources. We investigate these dual aspects of individual choice in networked games where resources undergo regime shifts between discrete quality states (viable or depleted) depending on collective extraction levels. We study the patterns of extraction that emerge on various network types when agents are free to vary extraction from each CPR separately to maximize their short-term payoffs. Using these results as a basis for comparison, we then investigate how results are altered if agents fix one aspect of adaptation (magnitude or allocation) while letting the other vary. We consider two constrained adaptation strategies: uniform adaptation, whereby agents adjust their extraction levels from all CPRs by the same amount, and reallocation, whereby agents selectively shift effort from lower- to higher-quality resources. A preference for uniform adaptation increases collective wealth on degree-heterogeneous agent-resource networks. Further, low-degree agents retain preferences for these constrained strategies under reinforcement learning. Empirical studies have indicated that some CPR appropriators ignore—while others emphasize—allocation aspects of adaptation; our results demonstrate that structural patterns of resource access can determine which behavior is more advantageous. |
| Date: | 2021–11–08 |
| URL: | http://d.repec.org/n?u=RePEc:osf:socarx:wmtqk&r=gth |
| By: | Rémi Suchon; Vincent Théroude |
| Abstract: | We build a dataset based on 23 experiments that introduce heterogeneous endowments into linear public good games. We use it to measure the effect of inequality on cooperation. This method allows an investigation of a large panel of inequality scenarios, with maximum representativeness in terms of the strength of inequality and design features. It offers the possibility to study the effect of the strength of inequality, a distinctive feature of our paper compared to the past experimental literature which has focused mainly on the existence of inequality. We also explore the contribution gaps between the relatively rich and relatively poor in heterogeneous groups. We discuss the interaction of time (dynamics) and punishment with inequality. We find that not only the presence, but also the strength of inequality has a negative impact on cooperation, but that the marginal effect becomes less negative as the level of inequality increases. We find that the rich contribute more than the poor in absolute amounts, while the poor contribute more as a proportion of their endowment. Both these gaps increase with the strength of inequality. Finally, punishment strongly attenuates the effect of inequality on aggregate cooperation, but has contrasted effects on the contribution gaps between the rich and the poor. There is no significant effect of inequality on the dynamics of contributions. |
| Keywords: | Public good game, cooperation, inequality, meta-analysis. |
| JEL: | C92 H41 D91 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ulp:sbbeta:2022-29&r=gth |
| By: | Lucas Baudin (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique); Rida Laraki (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique) |
| Date: | 2022–07–17 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03767937&r=gth |
| By: | Michelle R. Garfinkel; Constantinos Syropoulos |
| Abstract: | We consider a dynamic setting in which two sovereign states with overlapping ownership claims on a resource/asset first arm and then choose whether to resolve their dispute violently through war or peacefully through settlement. Both approaches depend on the states’ military capacities, but have very different outcomes. War precludes the possibility of international trade and can be destructive; however, once a winner is declared, arming is unnecessary in future periods. By contrast, a peaceful resolution avoids destruction and supports mutually advantageous trade; yet, settlements must be renegotiated in the shadow of arming and the threat of war. In this setting, we characterize the conditions under which peace arises as a stable equilibrium over time. We find that, depending on the destructiveness of war, time preferences, and the initial distribution of resource endowments, greater gains from trade can reduce arming and pacify international tensions. Even when the gains from trade are relatively small, peace might be sustainable, but only for more uneven endowment distributions. |
| Keywords: | interstate war, armed peace, unarmed peace, security policies, gains from trade, shadow of the future |
| JEL: | C72 C78 D30 D70 D74 F10 F51 F60 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10040&r=gth |
| By: | Strausz, Roland (HU Berlin) |
| Abstract: | A multi-product monopolist sells sequentially to a buyer who privately learns his valuations. Using big data, the monopolist learns the intertemporal correlation of the buyer’s valuations. Perfect price discrimination is generally unattainable—even when the seller learns the correlation perfectly, has full commitment, and in the limit where the consumption good about which the buyer has ex ante private information becomes insignificant. This impossibility is due to informational externalities which re- quires information rents for the buyer’s later consumption. These rents induce upward and downward distortions, violating the generalized no distortion at the top principle of dynamic mechanism design. |
| JEL: | D82 L52 |
| Date: | 2022–11–10 |
| URL: | http://d.repec.org/n?u=RePEc:rco:dpaper:347&r=gth |