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on Game Theory |
| By: | Ovanes Petrosian (National Research University Higher School of Economics) |
| Abstract: | This paper presents a complete description and the results of the Looking Forward Approach for cooperative differential games with transferable utility. The approach is used for constructing game theoretical models and defining solutions for conflict-controlled processes where information about the process updates dynamically or for differential games with dynamic updating. It is supposed that players lack certain information about the dynamical system and payoff function over the whole time interval on which the game is played. At each instant, information about the game structure updates, players receive new updated information about the dynamical system and payoff functions. A resource extraction game serves as an illustration in order to compare a cooperative trajectory, imputations, and the imputation distribution procedure in a game with the Looking Forward Approach and in the original game with a prescribed duration. |
| Keywords: | Differential Games, Cooperative Differential Games, Looking Forward Approach, Time Consistency, Strong Time Consistency. |
| JEL: | C71 C73 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:hig:wpaper:183/ec/2018&r=gth |
| By: | Bezalel Peleg; Ron Holzman |
| Abstract: | We survey the results on representations of committees and constitutions by game forms that possess some kind of equilibrium strategies for each profile of preferences of the players. The survey is restricted to discrete models, that is, we deal with finitely many players and alternatives. No prior knowledge of social choice is assumed: As far as definitions are concerned, the paper is self-contained. Section 2 supplies the necessary general tools for the rest of the paper. Each definition is followed by a simple (but nontrivial) example. In Section 3 we give a complete account of representations of committees (proper and monotonic simple games), by exactly and strongly consistent social choice functions. We start with Peleg's representations of weak games, and then provide a complete and detailed account of Holzman's solution of the representation problem for simple games without veto players. In Section 4 we deal with representations of constitutions by game forms. Following Gärdenfors we model a constitution by a monotonic and super additive effectivity function. We fully characterize the representations for three kinds of equilibrium: Nash equilibrium; acceptable equilibrium (Pareto optimal Nash equilibrium); and strong Nash equilibrium. We conclude in Section 5 with a report on two recent works on representations of constitutions under incomplete information. |
| Date: | 2018–02 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp715&r=gth |
| By: | Kenju Kamei |
| Abstract: | A rich body of literature has proposed that pairs behave significantly differently from individuals due to a number of reasons such as group polarization. This paper experimentally compares cooperation behaviors between pairs and individuals in a finitely-repeated two-player public goods game (continuous prisoner’s dilemma game). We show that pairs contribute significantly more than individuals to their group accounts. Especially when two pairs are matched with each other for the entire periods, they successfully build long-lasting cooperative relationships with their matched pairs. Our detailed analyses suggest that the enhanced cooperation behavior of pairs may be driven by (a) the mere fact that they have partners as decision-making units when they make decisions, (b) group polarization – those who initially prefer to contribute smaller amounts are more affected by the partners in their pairs, and (c) stronger conditional cooperation behavior of pairs to their matched pairs.Length: 51 pages |
| URL: | http://d.repec.org/n?u=RePEc:tcr:wpaper:e91&r=gth |
| By: | Yue Feng (Department of Economics, The University of Kansas); Tarun Sabarwal (Department of Economics, University of Kansas) |
| Abstract: | Echenique (2004) concludes that extensive form games with strategic complementarities are a very restrictive class of games. In the context of two stage, 2 × 2 games, we find that the restrictiveness imposed by quasisupermodularity and single crossing property is particularly severe, in the sense that the set of games in which payoffs satisfy these conditions has measure zero. In contrast, the set of such games that exhibit strategic complements (in the sense of increasing best responses) has infinite measure. Our characterization allows one to write uncountably many examples of two stage, 2 × 2 games with strategic complements. The results show a need to go beyond a direct application of quasisupermodularity and single crossing property to define strategic complements in extensive form games. |
| Keywords: | Strategic complements, extensive form game, two stage game |
| JEL: | C61 C70 |
| Date: | 2018–02 |
| URL: | http://d.repec.org/n?u=RePEc:kan:wpaper:201801&r=gth |
| By: | Stienen, V.F.; Engwerda, Jacob (Tilburg University, Center For Economic Research) |
| Abstract: | In this paper we try to quantify/measure the main factors that influence the equilibrium outcome and pursued strategies in a simplistic model for the use of fossil versus green energy over time. The model is derived using the standard Solow macro-economic growth model in a two-country setting within a dynamic game perspective. After calibrating the model for a setting of OECD versus non-OECD countries we study what kind of uncertainties affect the outcomes of the linearized model most, assuming both countries use Nash strategies to cope with shocks that impact the model. The main outcome of this study is that the parameters that occur in the objective of both players seem to carry the most uncertainty for both the outcome of the model and strategies. |
| Keywords: | Differential games; environemental engineering; uncertain dynamic systems; linearization; economic systems; open-loop control systems |
| JEL: | Q43 Q54 Q56 Q58 C61 C72 C73 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiucen:64079c75-c3cd-40d7-a722-6f961380ad96&r=gth |
| By: | Tomoya Kazumura; Debasis Mishra; Shigehiro Serizawa |
| Abstract: | A seller is selling multiple objects to a set of agents. Each agent can buy at most one object and his utility over consumption bundles (i.e., (object,transfer) pairs) need not be quasilinear. The seller considers the following desiderata for her (allocation) rule, which she terms desirable: (1) strategy-proofness, (2) ex-post individual rationality, (3) equal treatment of equals, (4) no wastage (every object is allocated to some agent). The minimum Walrasian equilibrium price (MWEP) rule is desirable. We show that at each preference profile, the MWEP rule generates more revenue for the seller than any desirable rule satisfying no subsidy. Our result works for quasilinear domain, where the MWEP rule is the VCG rule, and for various non-quasilinear domains, some of which incorporate positive income effect of agents. We can relax no subsidy to no bankruptcy in our result for certain domains with positive income effect. |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:tcr:wpaper:e116&r=gth |
| By: | Hitoshi Matsushima (The University of Tokyo) |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2017cf1076&r=gth |
| By: | Seigo Uchida; Masakazu Fukuzumi |
| Abstract: | We present complete results pertaining to the dynamical stability for sender-receiver games following Lewis (1969), and Nowak and Krakauer (1999) under the selection-mutation dynamics. Our research reveals that two distinct classes of neutrally stable strategies have a distinguishing feature of the dynamic stability. The rest points close to the strategies of these classes are asymptotically stable and all rest points other than these are not.Length: 47 pages |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:tcr:wpaper:e115&r=gth |
| By: | Agnes Cseh (Institute of Economics, Research Centre for Economic and Regional Studies, Hungarian Academy of Sciences, and Corvinus University of Budapest); Chien-Chung Huang (Ecole Normale Superieure, Paris, France); Telikepalli Kavitha (Tata Institute of Fundamental Research, Mumbai, India) |
| Abstract: | We are given a bipartite graph G = (A[B;E) where each vertex has a preference list ranking its neighbors: in particular, every a 2 A ranks its neighbors in a strict order of preference, whereas the preference list of any b 2 B may contain ties. A matching M is popular if there is no matching M0 such that the number of vertices that prefer M0 to M exceeds the number of vertices that prefer M to M0. We show that the problem of deciding whether G admits a popular matching or not is NP-hard. This is the case even when every b 2 B either has a strict preference list or puts all its neighbors into a single tie. In contrast, we show that the problem becomes polynomially solvable in the case when each b 2 B puts all its neighbors into a single tie. That is, all neighbors of b are tied in b's list and b desires to be matched to any of them. Our main result is an O(n2) algorithm (where n = jA [ Bj) for the popular matching problem in this model. Note that this model is quite di erent from the model where vertices in B have no preferences and do not care whether they are matched or not. |
| Keywords: | popular matching, NP-complete, polynomial algorithm, ties |
| JEL: | C63 C78 |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1723&r=gth |
| By: | Yusuke Matsuki |
| Abstract: | Abstract This study develops a simple distribution-free test of monotonicity of conditional expectations. The test is based solely on ordinary least squares (OLS) and exploits the property between conditional expectation and projection; we prove that the monotonicity of a conditional expectation function restricts the sign of a corresponding projection coefficient. The estimated projection coefficient is used for a one-tailed t-test. The test -- which is notably simpler than other monotonicity tests -- is applied to bidding data from Japanese construction procurement auctions to empirically test first-price sealed bid auction models with independent private values (IPV), assuming the data are generated from a symmetric Bayesian Nash equilibrium. We regress the bid level on the number of bidders and use the estimated projection coefficient for testing. We find that the test results depend on public work categories.Length: 25 pages |
| URL: | http://d.repec.org/n?u=RePEc:tcr:wpaper:e110&r=gth |
| By: | Ghidoni, Riccardo (Tilburg University, Center For Economic Research); Cleave, Blair (Tilburg University, Center For Economic Research); Suetens, Sigrid (Tilburg University, Center For Economic Research) |
| Abstract: | This paper focuses on social dilemma games where players may or may not meet the same partner again in the future. In line with the notion that contagion of cooperation is more likely the higher the likelihood of being re-matched with the same partner in the future, both a novel experiment and a meta-study document higher cooperation rates if this likelihoodis sufficiently high. |
| Keywords: | cooperation; contagion; matching protocol; laboratory experiment; meta-study |
| JEL: | C70 C90 D70 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiucen:6e947bbf-ab44-4e6e-89ec-c0fb414e8858&r=gth |
| By: | Agnes Cseh (Institute of Economics, Research Centre for Economic and Regional Studies, Hungarian Academy of Sciences, and Corvinus University of Budapest); Telikepalli Kavitha (Tata Institute of Fundamental Research, Mumbai, India) |
| Abstract: | Abstract Given a bipartite graph G=(A[B;E) with strict preference lists and given an edge e 2 E, we ask if there exists a popular matching in G that contains e. We call this the popular edge problem. A matching M is popular if there is no matching M0 such that the vertices that preferM0 toM outnumber those that preferM toM0. It is known that every stable matching is popular; however G may have no stable matching with the edge e. In this paper we identify another natural subclass of popular matchings called “dominant matchings” and show that if there is a popular matching that contains the edge e, then there is either a stable matching that contains e or a dominant matching that contains e. This allows us to design a linear time algorithm for identifying the set of popular edges. When preference lists are complete, we show an O(n3) algorithm to find a popular matching containing a given set of edges or report that none exists, where n = jAj+jBj. |
| Keywords: | popular matching, matching under preferences, dominant matching |
| JEL: | C63 C78 |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1725&r=gth |
| By: | Madhav Raghavan |
| Abstract: | We consider a model in which projects are to be assigned to agents based on their preferences, and where projects have capacities, i.e., can each be assigned to a minimum and maximum number of agents. The extreme cases of our model are the social choice model (the same project is assigned to all agents) and the house allocation model (each project is assigned to at most one agent). We show that, with general capacities,an allocation rule satis es strategy-proofness, group-non-bossiness, limited in uence, unanimity, and neutrality, if and only if it is a strong serial priority rule. A strong serial priority rule is a natural extension of a dictatorial rule (from the social choice model) and a serial priority rule (from the house allocation model). Our result thus provides a bridge between the characterisations in Gibbard (1973, \Manipulation of voting schemes: A general result", Econometrica, 41, 587-601), Satterthwaite (1975,Strategy-proofness and Arrow's Conditions: Existence and correspondence theorems for voting procedures and social welfare functions", Journal of Economic Theory, 10,187-216) and Svensson (1999, \Strategy-proof allocation of indivisible goods", Social Choice and Welfare, 16, 557-567). |
| JEL: | C78 D71 |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:lau:crdeep:17.17&r=gth |
| By: | Agnes Cseh (Institute of Economics, Research Centre for Economic and Regional Studies, Hungarian Academy of Sciences, and Corvinus University of Budapest); Robert W. Irving (School of Computing Science, University of Glasgow); David F. Manlove (School of Computing Science, Sir Alwyn Williams Building, University of Glasgow) |
| Abstract: | We consider two variants of the classical Stable Roommates problem with Incomplete (but strictly ordered) preference lists (sri) that are degree constrained, i.e., preference lists are of bounded length. The first variant, egal d-sri, involves finding an egalitarian stable matching in solvable instances of sri with preference lists of length at most d. We show that this problem is NP-hard even if d = 3. On the positive side we give a 2d+3 7 -approximation algorithm for d 2 {3, 4, 5} which improves on the known bound of 2 for the unbounded preference list case. In the second variant of sri, called d-srti, preference lists can include ties and are of length at most d. We show that the problem of deciding whether an instance of d-srti admits a stable matching is NP-complete even if d = 3. We also consider the “most stable” version of this problem and prove a strong inapproximability bound for the d = 3 case. However for d = 2 we show that the latter problem can be solved in polynomial time. |
| Keywords: | stable matching, bounded length preference lists, complexity, approximation algorithm |
| JEL: | C63 C78 |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1726&r=gth |
| By: | Sharma, Ajay |
| Abstract: | This paper demonstrates that in a duopoly model with firms being concerned about profit as well as corporate social responsibility (CSR), the outcome of game may coincide with the Stackelberg outcome. We argue that owner of the firm may use CSR orientation as a strategy to become Stackelberg leader in the quantity competition game. |
| Keywords: | Stackelberg outcome; Corporate social responsibility; Cournot game; Duopoly; Non-profit orientation |
| JEL: | D21 D43 L10 L20 |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:84326&r=gth |
| By: | Chung, Jeahan; Kim, Jeong-Yoo |
| Abstract: | The authors develop a model of cheap talk with multiple speakers in the presence of network externalities so that their utility functions are increasing in the network size. They first show that if there is no noise in private information that each sender receives, the full information is revealed by the harshest cross-checking strategies, that is, strategies to punish the senders unless their messages exactly coincide. Then, the authors show that with even a small noise cross-checking strategies cannot induce full revelation if utility functions of senders are linear in the network size, while full revelation is possible if utility functions are strictly concave. They find a sufficient condition for the existence of a fully revealing equilibrium which is supported by the cross-checking strategy with a positive confidence interval independent of each sender's private information. |
| Keywords: | cheap talk,cross-checking strategy,fully revealing equilibrium,network externality,word-of-mouth communication |
| JEL: | C7 D8 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:ifwedp:20189&r=gth |
| By: | Lin, Yu-Hsuan |
| Abstract: | This chapter examines the impact of inequality-averse attitudes on the individual incentives of participating in international environmental agreements by a laboratory experiment. The experimental result shows that the inequality-averse attitudes have significantly positive impact on the incentives of participation. Particularly, when they are non-critical players, egalitarians are likely to give up the free riding benefit by joining a coalition. It helps us to understand the coalition formation in the international conventions. |
| Keywords: | Social preference, experimental design, international environmental agreement, inequality aversion, heterogeneous countries |
| JEL: | C91 D71 Q01 Q54 Q58 |
| Date: | 2017–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:84097&r=gth |
| By: | David K Levine |
| Date: | 2018–01–15 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levarc:786969000000001441&r=gth |
| By: | Bernd (B.) Heidergott (VU Amsterdam, The Netherlands); Jia-Ping Huang (Shenzhen University, China); Ines (I.) Lindner (VU Amsterdam, The Netherlands) |
| Abstract: | We study social learning in a social network setting where agents receive independent noisy signals about the truth. Agents naïvely update beliefs by repeatedly taking weighted averages of neighbors' opinions. The weights are fixed in the sense of representing average frequency and intensity of social interaction. However, the way people communicate is random such that agents do not update their belief in exactly the same way at every point in time. We show that even if the social network does not privilege any agent in terms of influence, a large society almost always fails to converge to the truth. We conclude that wisdom of crowds is an illusive concept and bares the danger of mistaking consensus for truth. |
| Keywords: | Wisdom of crowds; social networks; information cascades; naive learning |
| JEL: | D83 D85 C63 |
| Date: | 2018–02–28 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20180018&r=gth |
| By: | Tilman Börgers; Jiangtao Li |
| Abstract: | We define and investigate a property of mechanisms that we call “strategic simplicity,” and that is meant to capture the idea that, in strategically simple mechanisms, strategic choices are easy. We define a mechanism to be strategically simple if strategic choices can be based on first-order beliefs about the other agents’ preferences alone, and there is no need for agents to form higher-order beliefs, because such beliefs are irrelevant to agents’ optimal choices. All dominant strategy mechanisms are strategically simple. But many more mechanisms are strategically simple. In particular, strategically simple mechanisms may be more flexible than dominant strategy mechanisms in the voting problem and the bilateral trade problem.. |
| JEL: | D82 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_6844&r=gth |
| By: | Ashwin Arulselvan (Department of Management Science, Sir William Duncan Building, University of Strathclyde); Agnes Cseh (Institute of Economics, Research Centre for Economic and Regional Studies, Hungarian Academy of Sciences, and Corvinus University of Budapest); Martin Groß (Institute for Mathematics, Technische Universität Berlin); David F. Manlove (School of Computing Science, Sir Alwyn Williams Building, University of Glasgow); Jannik Matuschke (TUM School of Management, Technische Universiät München) |
| Abstract: | We study a natural generalization of the maximum weight many-to- one matching problem. We are given an undirected bipartite graph G = (A[_ P;E) with weights on the edges in E, and with lower and upper quotas on the vertices in P.We seek a maximum weight many-to-one matching satisfying two sets of constraints: vertices in A are incident to at most one matching edge, while vertices in P are either unmatched or they are incident to a number of matching edges between their lower and upper quota. This problem, which we call maximum weight many-to-one matching with lower and upper quotas (wmlq), has applications to the assignment of students to projects within university courses, where there are constraints on the minimum and maximum numbers of students that must be assigned to each project. In this paper, we provide a comprehensive analysis of the complexity of wmlq from the viewpoints of classical polynomial time algorithms, xedparameter tractability, as well as approximability. We draw the line between NP-hard and polynomially tractable instances in terms of degree and quota constraints and provide ecient algorithms to solve the tractable ones. We further show that the problem can be solved in polynomial time for instances with bounded treewidth; however, the corresponding runtime is exponential in the treewidth with the maximum upper quota umax as basis, and we prove that this dependence is necessary unless FPT = W[1]. The approximability of wmlq is also discussed: we present an approximation algorithm for the general case with performance guarantee umax + 1, which is asymptotically best possible unless P = NP. Finally, we elaborate on how most of our positive results carry over to matchings in arbitrary graphs with lower quotas. |
| Keywords: | maximum matching, many-to-one matching, project allocation, inapproximability, bounded treewidth |
| JEL: | C63 C78 |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1724&r=gth |
| By: | Gutierrezy, Federico H. |
| Abstract: | This paper presents a new model of the household that is able to explain a variety of consumption patterns that existing models cannot describe, most notably, those associated with the Deaton and Paxson (1998) paradox. The most distinctive feature of this model is the presence of common-pool goods (rival and non-excludable) previously ignored in the literature. Under regularity conditions, the model can be interpreted as a hybrid between non-cooperative and a collective models of the household. Empirically, the paper revisits the Deaton-Paxson paradox exploiting household splits in longitudinal data and computes the elusive indifference scales coefficients. |
| Keywords: | sharing model,collective model,intra-household allocation,Deaton-Paxson paradox,household economies of scale,indifference scales |
| JEL: | D13 J12 O15 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:glodps:166&r=gth |
| By: | Olivier Sterck |
| Abstract: | Henderson et al. (2018) assessed the economic importance of 24 geographic variables in determining the worldwide spatial distribution of economic activity, as proxied by night lights. In this short piece, I first show that the method they used to measure the economic importance of effects - the Shapley value - is flawed, implying that some their results are misleading. Second, I use an axiomatic approach to build a new method for assessing the economic importance of effects, which corrects for the identified flaws. Finally, I revisit the conclusions of Henderson et al. (2018) in light of the new method. |
| Keywords: | Economic importance; Shapley values; Development; Physical geography; Agriculture |
| JEL: | B4 C18 O13 R12 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:csa:wpaper:2018-01&r=gth |