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on Game Theory |
| By: | Alexander Aurell; Gustav Karreskog |
| Abstract: | It is common to model learning in games so that either a deterministic process or a finite state Markov chain describes the evolution of play. Such processes can however produce undesired outputs, where the players' behavior is heavily influenced by the modeling. In simulations we see how the assumptions in (Young, 1993), a well-studied model for stochastic stability, lead to unexpected behavior in games without strict equilibria, such as Matching Pennies. The behavior should be considered a modeling artifact. In this paper we propose a continuous-state space model for learning in games that can converge to mixed Nash equilibria, the Recency Weighted Sampler (RWS). The RWS is similar in spirit Young's model, but introduces a notion of best response where the players sample from a recency weighted history of interactions. We derive properties of the RWS which are known to hold for finite-state space models of adaptive play, such as the convergence to and existence of a unique invariant distribution of the process, and the concentration of that distribution on minimal CURB blocks. Then, we establish conditions under which the RWS process concentrates on mixed Nash equilibria inside minimal CURB blocks. While deriving the results, we develop a methodology that is relevant for a larger class of continuous state space learning models. |
| Date: | 2020–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2009.12910&r=all |
| By: | Sebastien Courtin (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR1 - Université de Rennes 1 - UNIV-RENNES - Université de Rennes - CNRS - Centre National de la Recherche Scientifique); Rodrigue Tido Takeng (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR1 - Université de Rennes 1 - UNIV-RENNES - Université de Rennes - CNRS - Centre National de la Recherche Scientifique); Frédéric Chantreuil (UNC - Université de la Nouvelle-Calédonie) |
| Abstract: | In cooperative game theory, the concept of interaction index is an extension of the concept of value, considering interaction among players. In this paper we focus on cardinal-probabilistic interaction indices which are generalizations of the class of semivalues. We provide two types of decompositions. With the first one, a cardinal-probabilistic interaction index for a given coalition equals the difference between its external interaction index (or co-Möbius transfom) and a weighted sum of the individual impact of the remaining players on the interaction index of the considered coalition. The second decomposition, based on the notion of the "decomposer", splits an interaction index into a direct part, the decomposer, which measures the interaction in the coalition considered, and an indirect part, which indicates how all remaining players individually affect the interaction of the coalition considered. We propose alternative characterization of the cardinal-probabilistic interaction indices. We then propose an illustration with a well-known example in Multicriteria Aid for Decisions. |
| Keywords: | Game theory,Multicriteria Aid for Decisions,Cardinal-probabilistic interaction indices,External interaction index JEL Codes: C71 |
| Date: | 2020–08–22 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-02952516&r=all |
| By: | Kenju Kamei (Durham University Business School); Artem Nesterov (Durham University Business School) |
| Abstract: | Exogenously given reputational information is known to improve cooperation. This paper experimentally studies how people create such information through reporting of partner’s action choices, and whether the endogenous monitoring helps sustain cooperation, in an indefinitely repeated prisoner’s dilemma game. The experiment results show that most subjects report their opponents’ action choices, thereby successfully cooperating with each other, when reporting does not involve a cost. However, subjects are strongly discouraged from reporting when doing so is costly. As a result, they fail to achieve strong cooperation norms when the reported information is privately conveyed only to their next-round interaction partner. Costly reporting occurs only occasionally, even when there is a public record whereby all future partners can check the reported information. However, groups can then foster cooperation norms aided by the public record, because reported information gets gradually accumulated and becomes more informative over time. These findings suggest that the efficacy of endogenous monitoring depends on the quality of platforms that store reported information. |
| Keywords: | experiment, cooperation, prisoner’s dilemma game, reputation, reporting, infinitely repeated game. |
| JEL: | C92 C73 D70 H41 |
| Date: | 2020–09 |
| URL: | http://d.repec.org/n?u=RePEc:dur:durham:2020_02&r=all |
| By: | Jagu, E.; Massol, O. |
| Abstract: | This paper examines the deployment of a shared CO2 transportation infrastructure needed to support the combined emergence of Bio-energy with Carbon Capture and Storage (BECCS) and Fossil energy with Carbon Capture and Storage (CCS). We develop a cooperative game-theoretic approach to: (i) examine the conditions needed for its construction to be decided, and (ii) determine the break-even CO2 value needed to build such a shared infrastructure. In particular, we highlight that, as biogenic emissions are overlooked in currently-implemented carbon accounting frameworks, BECCS and CCS emitters face asymmetric conditions for joining a shared infrastructure. We thus further examine the influence of these carbon accounting considerations by assessing and comparing the break-even CO2 values obtained under alternative accounting rules. We apply this modeling framework to a large contemporary BECCS/CCS case-study in Sweden. Our results indicate that sustainable and incentive-compatible cooperation schemes can be implemented if the value of CO2 is high enough and show how that value varies depending on the carbon accounting framework retained for negative emissions and the nature of the infrastructure operators. In the most advantageous scenario, the CO2 value needs to reach 112€/tCO2, while the current Swedish carbon tax amounts to 110€/tCO2. Overall, these findings position pragmatic policy recommendations for local BECCS deployment. |
| Keywords: | Bio-energy with Carbon Capture and Storage; Negative emissions; CO2 transportation; infrastructure; cooperative game theory; carbon accounting |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:cty:dpaper:20/15&r=all |
| By: | M. Kleshnina; K. Kaveh; K. Chatterjee |
| Abstract: | Evolutionary game theory has proven to be an elegant framework providing many fruitful insights in population dynamics and human behaviour. Here, we focus on the aspect of behavioural plasticity and its effect on the evolution of populations. We consider games with only two strategies in both well-mixed infinite and finite populations settings. We assume that individuals might exhibit behavioural plasticity referred to as incompetence of players. We study the effect of such heterogeneity on the outcome of local interactions and, ultimately, on global competition. For instance, a strategy that was dominated before can become desirable from the selection perspective when behavioural plasticity is taken into account. Furthermore, it can ease conditions for a successful fixation in infinite populations' invasions. We demonstrate our findings on the examples of Prisoners' Dilemma and Snowdrift game, where we define conditions under which cooperation can be promoted. |
| Date: | 2020–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2009.13160&r=all |
| By: | Bergantiños, Gustavo; Moreno-Ternero, Juan D. |
| Abstract: | We take the axiomatic approach to uncover the structure of the revenue-sharing problem from broadcasting sports leagues. Our starting point is to explore the implications of three basic axioms: additivity, order preservation and weak upper bound. We show that the combination of these axioms characterizes a large family of rules, which is made of compromises between the uniform rule and concede-and-divide, such as the one represented by the equal-split rule. The members of the family are fully ranked according to the Lorenz dominance criterion, and the structure of the family guarantees the existence of a majority voting equilibrium. Strengthening some of the previous axioms, or adding new ones, we provide additional characterizations within the family. Weakening some of those axioms, we also characterize several families encompassing the original one. |
| Keywords: | resource allocation, broadcasting, sport leagues, axioms, concede-and-divide. |
| JEL: | C71 |
| Date: | 2020–09–28 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:103162&r=all |
| By: | Mohamed Belhaj (IMF-Midle East Center for Economics and Finance (CEF)); Renaud Bourlès (Aix-Marseille Univ, CNRS, Ecole Centrale, AMSE, Marseille, France); Frédéric Deroïan (Aix-Marseille Univ, CNRS, AMSE, Marseille, France) |
| Abstract: | We analyze risk-taking regulation when financial institutions are linked through shareholdings. We model regulation as an upper bound on institutions' default probability, and pin down the corresponding limits on risk-taking as a function of the shareholding network. We show that these limits depend on an original centrality measure that relies on the cross-shareholding network twice: (i) through a risk-sharing effect coming from complementarities in risk-taking and (ii) through a resource effect that creates heterogeneity among institutions. When risk is large, we find that the risk-sharing effect relies on a simple centrality measure: the ratio between Bonacich and self-loop centralities. More generally, we show that an increase in cross-shareholding increases optimal risk-taking through the risk-sharing effect, but that resource effect can be detrimental to some banks. We show how optimal risk-taking levels can be implemented through cash or capital requirements, and analyze complementary interventions through key-player analyses. We finally illustrate our model using real-world financial data and discuss extensions toward including debt-network, correlated investment portfolios and endogenous networks. |
| Keywords: | financial network, risk-taking, prudential regulation |
| JEL: | C72 D85 |
| Date: | 2020–09 |
| URL: | http://d.repec.org/n?u=RePEc:aim:wpaimx:2030&r=all |
| By: | Paolo Crosetto (GAEL [2020-....] - Laboratoire d'Economie Appliquée de Grenoble [2020-....] - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - UGA [2020-....] - Université Grenoble Alpes [2020-....] - Grenoble INP [2020-....] - Institut polytechnique de Grenoble - Grenoble Institute of Technology [2020-....] - UGA [2020-....] - Université Grenoble Alpes [2020-....]); Werner Güth (LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma], Max Planck Institute for Research on Collective Goods - Partenaires INRAE) |
| Abstract: | We study choices and reaction times of respondents in an impunity game with unfair offers. The non-private impunity game features two roles, proposer and respondent, who are both aware whether the pie size is small or large. Proposers decide among three more or less unfair offers; respondents can accept or reject the offer, in which case it is lost for them. Whatever the responder decides is communicated to the proposer. 240 proposers took part in a traditional laboratory; 24 respondents were in an fMRI setup where they confronted all 240 proposals elicited from proposers. Responses were sent via email to proposers. Proposers revealed little concern for respondents. Respondents overwhelmingly rejected small offers, especially from a large pie. Surprisingly and in contrast with most of the literature and the Social Heuristic Hypothesis, we find that on average acceptances took longer than rejections. This result is driven by individual heterogeneity. The rich response data allow us to distinguish different respondent types, finding a remarkable consistency: subjects mainly accepting (rejecting) take more time to reject (accept). We attribute this finding to heterogeneity in self-priming. Our results suggest a primary role for individual heterogeneity in experiments testing the intuitive or deliberate status of cooperation and altruism. |
| Keywords: | Impunity game,Social heuristic hypothesis,Response time,JEL codes: C72,C78,C91,D87 |
| Date: | 2020–09 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-02949346&r=all |
| By: | Roy, Sunanda; Singh, Rajesh; Weninger, Quinn |
| Abstract: | We present a model of firm entry in an industry that is managed with a production cap-and- trade (CAT) regulation. Firms are heterogeneous in productivity; each knows its own productivity but is uncertain about where it ranks in the entrant population. Entry is modeled as a simultaneous move game with incomplete information. Under CAT, firms compete to secure shares of the fixed permit supply. Entry payoffs are determined by own and rival entrant pro- ductivity; if average productivity of rival entrants is low, permit prices are low and returns to vested capital are high. The opposite holds when average productivity of rival entrants is high. We derive Bayesian Nash equilibrium entry and show that under certain conditions placement uncertainty increases entry, relative to a full information benchmark. We also obtain conditions under which this result is reversed. We extend the model to consider placement bias, i.e., firms believe they attain better than average productivity. Bias exacerbates the excess-entry problem. Our main finding, that placement uncertainty alone can cause excess market entry and inefficiency, has been overlooked in the literature. The new mechanism offers an alternative explanation for competitive blind spots in entrepreneurs. |
| Date: | 2020–01–31 |
| URL: | http://d.repec.org/n?u=RePEc:isu:genstf:202001310800001096&r=all |
| By: | Francisco Benita; Vittorio Bil\`o; Barnab\'e Monnot; Georgios Piliouras; Cosimo Vinci |
| Abstract: | We investigate traffic routing both from the perspective of real world data as well as theory. First, we reveal through data analytics a natural but previously uncaptured regularity of real world routing behavior. Agents only consider, in their strategy sets, paths whose free-flow costs (informally their lengths) are within a small multiplicative $(1+\theta)$ constant of the optimal free-flow cost path connecting their source and destination where $\theta\geq0$. In the case of Singapore, $\theta=1$ is a good estimate of agents' route (pre)selection mechanism. In contrast, in Pigou networks the ratio of the free-flow costs of the routes and thus $\theta$ is infinite, so although such worst case networks are mathematically simple they correspond to artificial routing scenarios with little resemblance to real world conditions, opening the possibility of proving much stronger Price of Anarchy guarantees by explicitly studying their dependency on $\theta$. We provide an exhaustive analysis of this question by providing provably tight bounds on PoA($\theta$) for arbitrary classes of cost functions both in the case of general congestion/routing games as well as in the special case of path-disjoint networks. For example, in the case of the standard Bureau of Public Roads (BPR) cost model, $c_e(x)= a_e x^4+b_e$ and more generally quartic cost functions, the standard PoA bound for $\theta=\infty$ is $2.1505$ (Roughgarden, 2003) and it is tight both for general networks as well as path-disjoint and even parallel-edge networks. In comparison, in the case of $\theta=1$, the PoA in the case of general networks is only $1.6994$, whereas for path-disjoint/parallel-edge networks is even smaller ($1.3652$), showing that both the route geometries as captured by the parameter $\theta$ as well as the network topology have significant effects on PoA (Figure 1). |
| Date: | 2020–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2009.12871&r=all |
| By: | Benjamin Golub; Stephen Morris |
| Abstract: | In coordination games and speculative over-the-counter financial markets, solutions depend on higher-order average expectations: agents' expectations about what counterparties, on average, expect their counterparties to think, etc. We offer a unified analysis of these objects and their limits, for general information structures, priors, and networks of counterparty relationships. Our key device is an interaction structure combining the network and agents' beliefs, which we analyze using Markov methods. This device allows us to nest classical beauty contests and network games within one model and unify their results. Two applications illustrate the techniques: The first characterizes when slight optimism about counterparties' average expectations leads to contagion of optimism and extreme asset prices. The second describes the tyranny of the least-informed: agents coordinating on the prior expectations of the one with the worst private information, despite all having nearly common certainty, based on precise private signals, of the ex post optimal action. |
| Date: | 2020–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2009.13802&r=all |
| By: | Lee, Jun Yeong; Hoffman, Elizabeth |
| Abstract: | This study investigates the impact of cheap talk on price in a repeated Bertrand oligopoly experiment. Each participant plays 20 rounds. Participants are placed in three-person bidding groups where the lowest bid wins. During the first 10 rounds, participants are not allowed to communicate with each other. All three-person groups converged to the zero-profit equilibrium in the first 10 periods. We then play another 10 rounds where participants can text with one another using an instant message system. Some groups were allowed to text before every round, some to text before every other round, some to text every third round, some to text every fourth round, and some to text only every fifth round. When texting is allowed, All groups attempt to collude to raise the price after being allowed to text, but the only groups who can maintain the higher price and converge over time to the joint-profit maximum are the groups who can text before every period. Hence, cheap talk is only effective when subjects can continuously monitor or converse. |
| Date: | 2020–05–01 |
| URL: | http://d.repec.org/n?u=RePEc:isu:genstf:202005010700001106&r=all |
| By: | Chia-Hui Chen; Junichiro Ishida; Wing Suen |
| Abstract: | This paper provides a general analysis of signaling under double-crossing preferences with a continuum of types. There are natural economic environments where indifference curves of two types cross twice, so that the celebrated single-crossing property fails to hold. Equilibrium exhibits a particular form of pooling: there is a threshold type below which types choose actions that are fully revealing and above which they choose actions that are clustered in possibly non-monotonic ways, with a gap separating these two sets of types. We also provide an algorithm to establish equilibrium existence by construction under mild conditions. |
| Date: | 2020–10 |
| URL: | http://d.repec.org/n?u=RePEc:dpr:wpaper:1103&r=all |
| By: | Daron Acemoglu; Georgy Egorov; Konstantin Sonin |
| Abstract: | In this essay, we provide a simple conceptual framework to elucidate the forces that lead to institutional persistence and change. Our framework is based on a dynamic game between different groups, who care both about current policies and institutions and future policies, which are themselves determined by current institutional choices, and clarifies the forces that lead to the most extreme form of institutional persistence (“institutional stasis”) and the potential drivers of institutional change. We further study the strategic stability of institutions, which arises when institutions persist because of fear of subsequent, less beneficial changes that would follow initial reforms. More importantly, we emphasize that, despite the popularity of ideas based on institutional stasis in the economics and political science literatures, most institutions are in a constant state of flux, but their trajectory may still be shaped by past institutional choices, thus exhibiting “path-dependent change”, so that initial conditions determine both the subsequent trajectories of institutions and how they respond to shocks. We conclude the essay by discussing how institutions can be designed to bolster stability, the relationship between social mobility and institutions, and the interplay between culture and institutions. |
| JEL: | C73 D72 D74 N10 N40 P16 |
| Date: | 2020–09 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:27852&r=all |