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on Game Theory |
| By: | Jiequn Han; Ruimeng Hu |
| Abstract: | We propose a deep neural network-based algorithm to identify the Markovian Nash equilibrium of general large $N$-player stochastic differential games. Following the idea of fictitious play, we recast the $N$-player game into $N$ decoupled decision problems (one for each player) and solve them iteratively. The individual decision problem is characterized by a semilinear Hamilton-Jacobi-Bellman equation, to solve which we employ the recently developed deep BSDE method. The resulted algorithm can solve large $N$-player games for which conventional numerical methods would suffer from the curse of dimensionality. Multiple numerical examples involving identical or heterogeneous agents, with risk-neutral or risk-sensitive objectives, are tested to validate the accuracy of the proposed algorithm in large group games. Even for a fifty-player game with the presence of common noise, the proposed algorithm still finds the approximate Nash equilibrium accurately, which, to our best knowledge, is difficult to achieve by other numerical algorithms. |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1912.01809&r=all |
| By: | Hokari, Toru (Faculty of Economics); Funaki, Yukihiko (School of Political Science and Economics); Sudhölter, Peter (Department of Business and Economics) |
| Abstract: | We show that neither Peleg's nor Tadenuma's well-known axiomatizations of the core by non-emptiness, individual rationality, super-additivity, and max consistency or complement consistency, respectively, hold when only convex rather than balanced TU games are considered, even if anonymity is required in addition. Moreover, we show that the core and its relative interior are only two solutions that satisfy Peleg's axioms together with anonymity and converse max consistency on the domain of convex games. |
| Keywords: | Convex TU game; core |
| JEL: | C71 |
| Date: | 2019–12–20 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:sdueko:2019_013&r=all |
| By: | Masaki Aoyagi (Osaka University); Seung Han Yoo (Department of Economics, Korea University, Seoul, Republic of Korea) |
| Abstract: | A platform matches agents from two sides of a market to create a trading opportunity between them. The agents subscribe to the platform by paying subscription fees which are contingent on their reported private types, and then engage in strategic interactions with their matched partner(s). A matching mechanism of the platform specifies the subscription fees as well as the matching rule which determines the probability that each type of agent on one side is matched with each type on the other side. We characterize optimal matching mechanisms which induce truthful reporting from the agents and maximize the subscription revenue. We show that the optimal mechanisms for a one-to-one trading platform match do not necessarily entail assortative matching, and may employ an alternative matching rule that maximizes the extraction of informational rents of the higher type. We then study an auction platform that matches each seller to two agents, and show that the optimal mechanism entails the combination of negative and positive assortative matching. |
| Keywords: | assortative, random, auction, subscription, revenue maximization, complementarity |
| JEL: | D42 D47 D62 D82 L12 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:iek:wpaper:1903&r=all |
| By: | Bos, Iwan; Marini, Marco A.; Saulle, Riccardo |
| Abstract: | Research on collusion in vertically differentiated markets is conducted under one or two potentially restrictive assumptions. Either there is a single industry-wide cartel or costs are assumed to be independent of quality or quantity. We explore the extent to which these assumptions are indeed restrictive by relaxing both. For a wide range of coalition structures, profit-maximizing cartels of any size price most of their lower quality products out of the market as long as production costs do not increase too much with quality. If these costs rise sufficiently, however, then market share is maintained for all product variants. All cartel sizes may emerge in equilibrium when exclusively considering individual deviations, but the industry-wide cartel is the only one immune to deviations by coalitions of members. Overall, our findings suggest that firms have a strong incentive to coordinate prices when the products involved are vertically differentiated. |
| Keywords: | Cartel Formation, Collusion, Vertical Differentiation, Endogenous Coalition Formation, Industry-wide Cartel, Partial Cartels. |
| JEL: | C70 C71 C72 D0 D01 D02 D04 D4 D42 D43 |
| Date: | 2019–12–23 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:97820&r=all |
| By: | Charles Mason (University of Wyoming) |
| Abstract: | I model International climate agreements among asymmetric countries, each of whom must select a profile of CO2 emissions over time. Predictions from this model imply larger reductions by "large" countries, but larger proportional reductions by "small" countries. I then analyze experimental data that sheds light on this issue. In contrast to the theoretical predictions, I find that smaller countries do not reduce emissions proportionately to their Nash level, and so the burden falls mostly on larger countries. Moreover, combined emissions are indistinguishable from the one-shot Nash emissions. This pessimistic outcome extends the commonly-found result in the literature that negotiations in similar repeated games (but with symmetric players) generally do not offer much hope for meaningful agreements, unless the effects are modest. One possible explanation for this pattern of results is inequality aversion. |
| Keywords: | Climate Negotiations, Repeated Game, Experiments |
| JEL: | D8 L15 |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:fae:wpaper:2019.22&r=all |
| By: | Paramahansa Pramanik; Alan M. Polansky |
| Abstract: | Mutually beneficial cooperation is a common part of economic systems as firms in partial cooperation with others can often make a higher sustainable profit. Though cooperative games were popular in 1950s, recent interest in non-cooperative games is prevalent despite the fact that cooperative bargaining seems to be more useful in economic and political applications. In this paper we assume that the strategy space and time are inseparable with respect to a contract. Under this assumption we show that the strategy spacetime is a dynamic curved Liouville-like 2-brane quantum gravity surface under asymmetric information and that traditional Euclidean geometry fails to give a proper feedback Nash equilibrium. Cooperation occurs when two firms' strategies fall into each other's influence curvature in this strategy spacetime. Small firms in an economy dominated by large firms are subject to the influence of large firms. We determine an optimal feedback semi-cooperation of the small firm in this case using a Liouville-Feynman path integral method. |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1912.12146&r=all |
| By: | Ortega, Josué; Segal-Halevi, Erel |
| Abstract: | In cake-cutting, strategy-proofness is a very costly requirement in terms of fairness: for n = 2 it implies a dictatorial allocation, whereas for n Ï 3 it requires that one agent receives no cake. We show that a weaker version of this property recently suggested by Troyan and Morril, called not-obvious manipulability, is compatible with the strong fairness property of proportionality, which guarantees that each agent receives 1/n of the cake. Both properties are satisfied by the leftmost leaves mechanism, an adaptation of the Dubins - Spanier moving knife procedure. Most other classical proportional mechanisms in literature are obviously manipulable, including the original moving knife mechanism. Not-obvious manipulability explains why leftmost leaves is manipulated less often in practice than other proportional mechanisms. |
| Keywords: | cake-cutting,not-obvious manipulability,prior-free mechanism design |
| JEL: | D63 D82 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:zewdip:19056&r=all |
| By: | Kazuya Kikuchi; Yukio Koriyama |
| Abstract: | This paper considers collective decision-making when individuals are partitioned into groups (e.g., states or parties) endowed with voting weights. We study a game in which each group chooses an internal rule that specifies the allocation of its weight to the alternatives as a function of its members' preferences. We show that under quite general conditions, the game is a Prisoner's Dilemma: while the winner-take-all rule is a dominant strategy, the equilibrium is Pareto dominated. We also show asymptotic Pareto dominance of the proportional rule. Our numerical computation for the US Electoral College verifies the sensibility of the asymptotic results. |
| Date: | 2019–06 |
| URL: | http://d.repec.org/n?u=RePEc:dpr:wpaper:1059r&r=all |
| By: | Zongxi Li; A. Max Reppen; Ronnie Sircar |
| Abstract: | We propose a mean field game model to study the question of how centralization of reward and computational power occur in the Bitcoin-like cryptocurrencies. Miners compete against each other for mining rewards by increasing their computational power. This leads to a novel mean field game of jump intensity control, which we solve explicitly for miners maximizing exponential utility, and handle numerically in the case of miners with power utilities. We show that the heterogeneity of their initial wealth distribution leads to greater imbalance of the reward distribution, or a "rich get richer" effect. This concentration phenomenon is aggravated by a higher bitcoin price, and reduced by competition. Additionally, an advanced miner with cost advantages such as access to cheaper electricity, contributes a significant amount of computational power in equilibrium. Hence, cost efficiency can also result in the type of centralization seen among miners of cryptocurrencies. |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1912.01952&r=all |
| By: | Adam Zylbersztejn (Univ Lyon, Université Lumière Lyon 2, GATE L-SE UMR 5824, 69130 Ecully, France); Zakaria Babutsidze (SKEMA Business School, Université Côte d'Azur (GREDEG) and OFCE, Sciences Po Paris); Nobuyuki Hanaki (Institute of Social and Economic Research, Osaka University) |
| Abstract: | We experimentally investigate how much value people put in observable information about others in strategic interactions. The incentivized experimental task is to predict an unknown target player's trustworthiness in an earlier hidden action game. In Experiment 1, we vary the source of information about the target player (neutral picture, neutral video, video containing strategic content). The observed prediction accuracy rates then serve as an empirical measure of the objective value of information. In Experiment 2, we elicit the subjective value of information using the standard stated preferences method ("willingness to accept"). While the elicited subjective values are ranked in the same manner as the objective ones, subjects attach value to information which does not help predict target behavior, and exaggerate the value of helpful information. |
| Keywords: | prediction, observable information, individual characteristics, stated preferences, willingness to accept, experiment |
| JEL: | C72 D83 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:gat:wpaper:1936&r=all |
| By: | Alessandro Doldi; Marco Frittelli |
| Abstract: | A Systemic Optimal Risk Transfer Equilibrium (SORTE) was introduced in "Systemic Optimal Risk Transfer Equilibrium" for the analysis of the equilibrium among financial institutions or in insurance-reinsurance markets. A SORTE conjugates the classical B\"uhlmann's notion of an equilibrium risk exchange with a capital allocation principle based on systemic expected utility optimization. In this paper we extend such notion to the case in which the value function to be optimized has two components, one being the sum of the single agents' utility functions, the other consisting of a truly systemic component. The latter could be either enforced by an external regulator or be agreed on by the participants in the market. Technically, the extension of SORTE to the new setup requires developing a theory for multivariate utility functions and selecting at the same time a suitable framework for the duality theory. Conceptually, this more general framework allows us to introduce and study a Nash Equilibrium property of the optimizer. We prove existence, uniqueness, Pareto optimality and the Nash Equilibrium property of the newly defined Multivariate Systemic Optimal Risk Transfer Equilibrium. |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1912.12226&r=all |
| By: | José Pedro Gaivão; Telmo Peixe |
| Abstract: | The Rock-Paper-Scissors (RPS) game is a classic non-cooperative game widely studied in terms of its theoretical analysisas well as in its applications,ranging from sociology and biology to economics. Many experimental results of the RPS game indicate that this game is better modelled by the discretized best-response dynamics rather than continuous time dynamics. In this work we show that the attractor of the discrete time best-response dynamics of the RPS game is finite and periodic.Moreover we also describe the bifurcations of the attractor and determine the exact number,period and location of the periodic strategies. |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:ise:remwps:wp01082019&r=all |
| By: | Jawwad Noor (e Department of Economics, Boston University) |
| Abstract: | Beliefs are intuitive if they rely on associative memory, which can be described as a network of associations between events. A belief-theoretic characterization of the model is provided, its uniqueness properties are established, and the intersection with the Bayesian model is characterized. The formation of intuitive beliefs is modelled after machine learning, whereby the network is shaped by past experience via minimization of the difference from an objective probability distribution. The model is shown to accommodate correlation misperception, the conjunction fallacy, base-rate neglect/conservatism, etc. |
| Keywords: | Beliefs, Intuition, Associative memory, Boltzmann machine, Energy-Based Neural Networks, Non-Bayesian updating |
| JEL: | C45 D01 D90 |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2216&r=all |
| By: | Zhang, Hanzhe (Michigan State University, Department of Economics) |
| Abstract: | This paper studies the use of posted prices versus auctions in a large dynamic market with many short-lived sellers and long-lived buyers. Although a reserve-price auction maximizes the expected revenue, the optimal revenue decreases when the market becomes more buyer-friendly; namely, when buyers survive longer, face fewer competitors, and become more patient. As the market becomes more buyer-friendly, the revenue advantage from a reserve-price auction over posting a price reduces, but using posted prices would lead to sale and allocative inefficiencies. |
| Keywords: | optimal sales mechanism; reserve-price auction; posted price |
| JEL: | D44 |
| Date: | 2019–12–17 |
| URL: | http://d.repec.org/n?u=RePEc:ris:msuecw:2019_013&r=all |
| By: | Panayotis Mertikopoulos (Université Grenoble Alpes); Heinrich H. Nax (Department of Humanities, Social and Political Sciences, Eidgenössische Technische Hochschule Zürich); Bary S. R. Pradelski (Université Grenoble Alpes) |
| Abstract: | We examine two-sided markets where players arrive stochastically over time and are drawn from a continuum of types. The cost of matching a client and provider varies, so a social planner is faced with two contending objectives: a) to reduce players’ waiting time before getting matched; and b) to form efficient pairs in order to reduce matching costs. We show that such markets are characterized by a quick or cheap dilemma: Under a large class of distributional assumptions, there is no `free lunch’, i.e., there exists no clearing schedule that is simultaneously optimal along both objectives. We further identify a unique breaking point signifying a stark reduction in matching cost contrasted by an increase in waiting time. Generalizing this model, we identify two regimes: one, where no free lunch exists; the other, where a window of opportunity opens to achieve a free lunch. Remarkably, greedy scheduling is never optimal in this setting. |
| Keywords: | Dynamic matching, Online markets, Market design |
| JEL: | D47 C78 C60 D80 |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2217&r=all |
| By: | José Pedro Pontes; Ana Paula Buhse |
| Abstract: | This paper tries to explain differences in high education growth across European countries by using a coordinantion game (Stag Hunt) played by n candidates to college education. The payoff of enrolling in the university is positive only if there is "unanimity" i.e. if all candidates engage in higher education, being zero otherwise. This coordination requirement follows from the specialized nature of skills acquired through higher education, which can only be made profitable if each graduate is matched with graduate complementary specialists. This game has two strict Nash equilibria, where either all youngsters enter the university or none does. We show that the assessment of the factors that explain the differential growth of universities across countries is related with alternative ways of selecting a Nash equilibrium in the coordination game. By using empirical data, we can conclude that demographic trends and a cumulative causation factor play a major role in tertiary education growth, while the "wage premium" associated with college attendance also matters but is relatively secondary. "Tuition fees" and other direct financial costs do not appear to be a significant cause or hindrance of university development. |
| Keywords: | Higher Education; Regional Development; Coordination Games; Risk Dominance. |
| JEL: | C72 I20 O12 R11 |
| Date: | 2019–12 |
| URL: | http://d.repec.org/n?u=RePEc:ise:remwps:wp01052019&r=all |