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on Game Theory |
| By: | Andrea Collevecchio; Hlafo Alfie Mimun; Matteo Quattropani; Marco Scarsini |
| Abstract: | We consider the class of two-person ordinal potential games where each player has the same number of actions $K$. Each game in this class admits at least one pure Nash equilibrium and the best-response dynamics converges to one of these pure Nash equilibria; which one depends on the starting point. So, each pure Nash equilibrium has a basin of attraction. We pick uniformly at random one game from this class and we study the joint distribution of the sizes of the basins of attraction. We provide an asymptotic exact value for the expected basin of attraction of each pure Nash equilibrium, when the number of actions $K$ goes to infinity. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.05460 |
| By: | Francesco Caruso (Università di Napoli Federico II); Maria Carmela Ceparano (Università di Napoli Federico II); Jacqueline Morgan (Università di Napoli Federico II and CSEF; University of Calabria, Institute for the Study of Labor (IZA)) |
| Abstract: | Both pessimistic and optimistic bilevel optimization problems may be not stable under perturbation when the lower-level problem has not a unique solution, meaning that the limit of sequences of solutions (resp. equilibria) to perturbed bilevel problems is not necessarily a solution (resp. an equilibrium) to the original problem. In this paper, we investigate the notion of lower Stackelberg equilibrium, an equilibrium concept arising as a limit point of pessimistic equilibria and of optimistic equilibria of perturbed bilevel problems. First, connections with pessimistic equilibria and optimistic equilibria are obtained in a general setting, together with existence and closure results. Secondly, the problem of finding a lower Stackelberg equilibrium is shown to be stable under general perturbation, differently from what happens for pessimistic and optimistic bilevel problems. Then, moving to the game theory viewpoint, the set of lower Stackelberg equilibria is proved to coincide with the set of subgame perfect Nash equilibrium outcomes of the associated Stackelberg game. These results allow to achieve a comprehensive look on various equilibrium concepts in bilevel optimization and in Stackelberg games as well as to add a new interpretation in terms of game theory to previous limit results on pessimistic equilibria and optimistic equilibria under perturbation. |
| Keywords: | Pessimistic and optimistic bilevel optimization problems; Stackelberg game; lower Stackelberg equilibrium; Subgame perfect Nash equilibrium; Stability under perturbation. |
| Date: | 2024–04–09 |
| URL: | https://d.repec.org/n?u=RePEc:sef:csefwp:715 |
| By: | Boczoń, Marta; Vespa, Emanuel; Weidman, Taylor; Wilson, Alistair J |
| Abstract: | Abstract: In repeated games, where both collusive and noncollusive outcomes can be supported as equilibria, it is crucial to understand the likelihood of selection for each type of equilibrium. Controlled experiments have empirically validated a selection criterion for the two-player repeated prisoner’s dilemma: the basin of attraction for always defect. This prediction device uses the game primitives to measure the set of beliefs for which an agent would prefer to unconditionally defect rather than attempt conditional cooperation. This belief measure reflects strategic uncertainty over others’ actions, where the prediction is for noncooperative outcomes when the basin measure is full, and cooperative outcomes when empty. We expand this selection notion to multi-player social dilemmas and experimentally test the predictions, manipulating both the total number of players and the payoff tensions. Our results affirm the model as a tool for predicting long-term cooperation, while also speaking to some limitations when dealing with first-time encounters. |
| Keywords: | Economics, Applied Economics, Economic Theory, Applied economics, Econometrics, Economic theory |
| Date: | 2024–07–05 |
| URL: | https://d.repec.org/n?u=RePEc:cdl:ucsdec:qt7pk7c4gb |
| By: | Toraubally, Waseem A. (Newcastle Business School) |
| Abstract: | We augment the Shapley–Shubik (1977) market game to include a spatial dimension à la Hotelling (1929). Taking firms’ locations as given, we study and characterise, through several propositions, lemmata, and a theorem, the main equilibrium predictions of this new model. When both firms locate in the centre and there is no product differentiation at all, we derive a counterexample in which both firms charge a price that is greater than marginal cost. Intriguingly, we show that even when both firms are in the same location, it is possible for the Law of One Price (LOOP) to fail, i.e., the exact same good sells at different prices across two platforms that are a priori identical. We derive similar (equal- and unequal-price) counterexamples in the context where the firms locate at the extreme ends of the city. Now, it is well known that in the traditional Hotelling model, a pure-strategy Nash equilibrium (PSNE) fails to exist when the two firms are closely spaced and near the centre of the city. In our main result, we allow the firms to be arbitrarily close to each other, and propose two counterexamples in which a PSNE exists. In one, the LOOP holds, while in the other, it fails. |
| Keywords: | Spatial Cournot oligopoly ; Existence of pure-strategy equilibrium with closely spaced firms ; Failure of Law of One Price ; Strategic behaviour with a continuum of players |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:wrk:wcreta:87 |
| By: | Lorenz Hartmann (University of Basel); David Kelsey (University of Nottingham) |
| Abstract: | This paper proposes that the ambiguity reflected by a set of priors remains unchanged when the set is translated within the probability simplex, i.e. ambiguity is location invariant. This unifies and generalises numerous influential definitions of ambiguity in the literature. Location invariance is applied to normal form games where players perceive strategic ambiguity. The set of translations of a given set of priors is shown to be isomorphic to the probability simplex. Thus considering mixtures of translations has a convexifying effect similar to considering mixed strategies in the absence of ambiguity. This leads to the proof of equilibrium existence in complete generality using a fixed point theorem. We illustrate the modelling capabilities of our solution concept and demonstrate how our model can intuitively describe strategic interaction under ambiguity. |
| Keywords: | ambiguity; multiple priors; translations; games; equilibrium existence |
| Date: | 2024–05 |
| URL: | https://d.repec.org/n?u=RePEc:not:notcdx:2024-05 |
| By: | Christiansen, Anna Gade (Department of Economics, Copenhagen Business School); Llorca, Manuel (Department of Economics, Copenhagen Business School); Jamasb, Tooraj (Department of Economics, Copenhagen Business School); Zhao, Tian (School of Economics and Management, Beihang University, China) |
| Abstract: | This paper investigates how energy networks in the European Union can be encouraged to increase innovation to reach the decarbonisation goals. We design and analyse a tripar-tite evolutionary game model with the European Commission, national energy regulators, and energy network companies being the groups of players in the game. We find that the only evolutionary stable state of the game is where the three groups of players choose cooperation strategies. For the Commission and the national regulatory authorities, induc-ing innovation involves adopting new policy and regulatory mechanisms, respectively. For the energy networks, it involves investing in innovation with decarbonisation goals. We assume that the initial probability of the Commission choosing its cooperation strategy is relatively high and the initial probabilities of the regulators and the energy networks choosing cooperation strategies is relatively low. Numerical simulations suggest that the convergence rate to the evolutionary stable state can be increased if the Commission in-creases the probability of energy networks receiving external funding and penalty im-posed on regulators to adapt their incentive mechanisms to induce innovation. The Com-mission clearly plays a key role in reaching the stable state. |
| Keywords: | Energy networks; innovation; regulation; green transition; tripartite evolutionary game |
| JEL: | C70 L50 L90 O30 Q40 Q50 |
| Date: | 2024–06–24 |
| URL: | https://d.repec.org/n?u=RePEc:hhs:cbsnow:2024_011 |
| By: | Atulya Jain; Vianney Perchet |
| Abstract: | How should an expert send forecasts to maximize her utility subject to passing a calibration test? We consider a dynamic game where an expert sends probabilistic forecasts to a decision maker. The decision maker uses a calibration test based on past outcomes to verify the expert's forecasts. We characterize the optimal forecasting strategy by reducing the dynamic game to a static persuasion problem. A distribution of forecasts is implementable by a calibrated strategy if and only if it is a mean-preserving contraction of the distribution of conditionals (honest forecasts). We characterize the value of information by comparing what an informed and uninformed expert can attain. Moreover, we consider a decision maker who uses regret minimization, instead of the calibration test, to take actions. We show that the expert can achieve the same payoff against a regret minimizer as under the calibration test, and in some instances, she can achieve strictly more. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.15680 |
| By: | Patrick Rey; Yossi Spiegel; Konrad O. Stahl |
| Abstract: | We study the feasibility and profitability of predation in a dynamic environment, using a parsimonious infinite-horizon, complete information setting in which an incumbent repeatedly faces potential entry. When a rival enters, the incumbent chooses whether to accommodate or predate it; the entrant then decides whether to stay or exit. We show that there always exists a Markov perfect equilibrium, which can be of three types: accommodation, monopolization, and recurrent predation. We then analyze and compare the welfare effects of different antitrust policies, accounting for the possibility that recurrent predation may be welfare improving. |
| Keywords: | predation, accommodation, entry, legal rules, Markov perfect equilibrium |
| JEL: | D43 L41 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11172 |
| By: | Christian Ewerhart |
| Abstract: | The n-player Tullock contest with complete information is known to admit explicit solutions in special cases, such as (i) homogeneous valuations, (ii) constant returns, and (iii) two contestants. But can that model be solved more generally? In this paper, we show that key characteristics of the equilibrium, such as individual efforts, winning probabilities, and payoffs cannot, in general, be expressed in terms of the primitives of the model using basic arithmetic operations plus the extraction of roots alone. In this sense, the Tullock contest is intractable. We argue that our formal concept of tractability captures the intuitive understanding of the notion. |
| Keywords: | Tullock contest, pure-strategy Nash equilibrium, solution by radicals, Galois theory |
| JEL: | C02 C72 D72 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:zur:econwp:447 |
| By: | Giorgio Fabbri (GAEL - Laboratoire d'Economie Appliquée de Grenoble - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes); Silvia Faggian (Université de Venise Ca’ Foscari | Università Ca’ Foscari di Venezia); Giuseppe Freni (PARTHENOPE - Università degli Studi di Napoli “Parthenope” = University of Naples) |
| Abstract: | This study examines the dynamics of the exploitation of a natural resource distributed among and flowing between several nodes connected via a weighted, directed network. The network represents the locations and interactions of the resource nodes. A regulator decides to designate some of the nodes as natural reserves where no exploitation is allowed. The remaining nodes are assigned (one‐to‐one) to players, who exploit the resource at the node. It is demonstrated how the equilibrium exploitation and resource stocks depend on the productivity of the resource sites, the structure of the connections between the sites, and the number and preferences of the agents. The best locations to host nature reserves are identified per the model's parameters and correspond to the most central (in the sense of eigenvector centrality) nodes of a suitably redefined network that considers the nodes' productivity. |
| Keywords: | Harvesting, spatial models, differential games, nature reserves |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-04612475 |
| By: | Alfred Anate Mayaki |
| Abstract: | In this paper the Nash equilibrium reversion is used as an optimal tool for clearing dynamic prices and wages. The balanced growth path of the efficiency wage and the outcome of repeated household and firm wage bargaining decisions are determined by various exogenous competitive rigidities. A location model is pursued to explore the extent to which a downstream spatial cooperation agreement might affect the price equilibrium. There is also an endogenous hiring function and a knowledge base which is increasing in output, as is the real wage. As the article demonstrates, after accounting for real rigidities in the baseline model the effect of wage growth on household utility through staggered bargaining can be best catered for by adopting a policy of point scoring on the mobility of skilled labour against the models key rigidities. Finally labour mobility is explored. Mobility point scores, which serve to encourage mobility from skilled labour within the model not only increase the knowledge base but also place upward pressure on nominal wage growth. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.18471 |
| By: | Jonathan Gehle; Ferdinand A. von Siemens; Ferdinand von Siemens |
| Abstract: | We investigate how heterogeneous social preferences affect the communication of painful information in social relationships. We characterize the existence conditions for a pooling equilibrium in which individuals conceal painful information because revealing the latter would signal that they are selfish, thereby leading to a loss of trust. We also find that compassionate individuals may then be more tempted to reveal bad news than selfish individuals because they benefit less from an intact social relationship. Moreover, there may be multiple equilibria with different degrees of information disclosure and standard equilibrium refinements have no bite. Coordination on an inefficient equilibrium could therefore lead to severe information frictions, even if the pain of receiving bad news is quite small. |
| Keywords: | communication, painful information, social preferences, trust |
| JEL: | D82 D83 D91 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11181 |
| By: | Shangshang Li |
| Abstract: | This paper evaluates gains from international monetary policy cooperation between the financial center and periphery countries in a two-country open economy model consistent with global financial cycles. Compared to the non-cooperative Nash equilibrium, the optimal cooperative equilibrium robustly fails to benefit both countries simultaneously. The financial periphery is more likely to gain from cooperation if it raises less foreign currency debt or is relatively small. These results also hold when considering the transitional gains and losses of moving from non-cooperation to cooperation. The uneven distribution of gains from cooperation persists when both countries adopt implementable policy rules with and without cooperation. Nevertheless, both countries gain when transitioning from the Nash to the cooperative implementable rules. Regardless of the financial center's policy, rules responding to the exchange rate dominate over purely inward-looking rules for the financial periphery. |
| Keywords: | policy cooperation, global financial cycle, currency mismatch |
| JEL: | F34 E52 F42 E44 E58 E61 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:wsr:wpaper:y:2024:m:07:i:199 |
| By: | Paulo Ramos; Thomas G. Wollmann |
| Abstract: | This paper uses an aggregative games framework to predict consumer welfare when market structure is endogenously determined. Our main results characterize mergers whose synergies reduce consumer welfare by inducing rivals to exit. The conditions under which such mergers arise are broad, regardless of whether we consider quantity competition among homogeneous products or price competition among multi-product firms facing multinomial logit demand. Calibrated models based on commonly used parameter values indicate that the synergies required to avoid consumer harm can be much higher than those implied by traditional merger analysis. Neither subsequent entry nor follow-on mergers necessarily mitigate the problem. |
| JEL: | D43 G34 K21 L13 |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:32630 |
| By: | Brian McFadden |
| Abstract: | A mechanism is described that addresses the fundamental trade off between media producers who want to increase reach and consumers who provide attention based on the rate of utility received, and where overreach negatively impacts that rate. An optimal solution can be achieved when the media source considers the impact of overreach in a cost function used in determining the optimal distribution of content to maximize individual consumer utility and participation. The result is a Nash equilibrium between producer and consumer that is also Pareto efficient. Comparison with the literature on Recommender systems highlights the advantages of the mechanism.The review suggests advancements over that literature including identifying an optimal content volume for the consumer and improvements for handling multiple objectives A practical algorithm to generate the optimal distribution for each consumer is provided. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.16212 |
| By: | Gustavo Bergantiños (ECOBAS, Universidade de Vigo); Christian Trudeau (Department of Economics, University of Windsor) |
| Abstract: | In Alcalde-Ulzu et al. (Journal of Economic Theory, 2022), a novel model to measure the value of a language is developed, and a family of value functions is axiomatically characterized. These functions assign the value of a language by looking at the groups that can communicate with that language. Each group is assigned a fixed value that depends on its size. If a group can communicate in a language, that language gets assigned the value associated to the group, divided by the number of languages commonly spoken by the group. We show that this family crucially depends on the monotonicity axiom used, and that a di¤erent interpretation leads to a vastly different family of functions, in which the value of a language is a simple function of its number of speakers. Specifically, the difference in the monotonicity axioms boils down to the following question: If a group shares a common language, is there any value in being able to communicate in another language? Our version, that we call Language inclusion monotonicity, says that there is. It leads to different policy implications, not necessarily favoring the majority languages. |
| Keywords: | value of language, communicative benefits, monotonicity, axiomatic analysis, |
| JEL: | C72 D61 D63 Z13 |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:wis:wpaper:2403 |
| By: | Andrew Koh; Sivakorn Sanguanmoo; Weijie Zhong |
| Abstract: | We provide a unified analysis of how dynamic information should be designed in optimal stopping problems: a principal controls the flow of information about a payoff relevant state to persuade an agent to stop at the right time, in the right state, and choose the right action. We further show that for arbitrary preferences, intertemporal commitment is unnecessary: optimal dynamic information designs can always be made revision-proof. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.12278 |