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on Game Theory |
| By: | Balázs Sziklai (Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences); Tamás Fleiner (Department of Computer Science and Information Theory, Budapest University of Technology and Economics); Tamás Solymosi (Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences) |
| Abstract: | There lies a network structure between fixed tree and minimum cost spanning tree networks that has not been previously analyzed from a cooperative game theoretic perspective, namely, directed acyclic graph (DAG) networks. In this paper we consider the cost allocation game defined on DAG-networks. We briefly discuss the relation of DAG-games with other network-based cost games. We demonstrate that in general a DAG-game is not concave, even its core might be empty, but we provide an efficiently verifiable condition satisfied by a large class of directed acyclic graphs that is sufficient for balancedness of the associated DAG-game. We introduce a network canonization process and prove various structural results for the core of canonized DAG-games. In particular, we characterize classes of coalitions that have a constant payoff in the core. In addition, we identify a subset of the coalitions that is sufficient to determine the core. |
| Keywords: | cooperative game theory, directed acyclic graphs, core, acyclic directed Steiner tree |
| JEL: | C71 |
| Date: | 2014–07 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1418&r=gth |
| By: | Litan, Cristian (Department of Statistics, Forecasting, Mathematics); Marhuenda, Francisco (Department of Economics); Sudhölter, Peter (Department of Business and Economics) |
| Abstract: | We show the generic finiteness of the number of probability distributions on outcomes induced by Nash equilibria for two-person game forms such that either (i) one of the players has no more than two strategies or (ii) both of the players have three strategies, and (iii) for outcome game forms with three players, each with at most two strategies. Finally, we exhibit an example of a game form with three outcomes and three players for which the Nash equilibria of the associated game induce a continuum of payoffs for an open non-empty set of utility profiles. |
| Keywords: | Outcome game form; Completely mixed Nash equilibrium; Generic finiteness |
| JEL: | C72 |
| Date: | 2014–11–05 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:sdueko:2014_017&r=gth |
| By: | Xiaochuan Huang (DT Captical Management Co., LTD.); Takehito Masuda (Research Center for Social Design Engineering, Kochi University of Technology); Yoshitaka Okano (Kochi University of Technology); Tatsuyoshi Saijo (Kochi University of Technology) |
| Abstract: | We develop the simplified approval mechanism (SAM) for n-player public good provision with binary choice. The SAM provides each cooperator a chance to revise his choice when players’ choices are not unanimous. Hence, players can easily retaliate against defection as widely proposed in repeated game theory or conditionally cooperate as observed in voluntary contribution game experiments. The SAM implements the cooperative outcome in backward elimination of weakly dominated strategies (BEWDS). The implementation result also holds in limit logit agent quantal response equilibrium (LAQRE). The average cooperation rate in the SAM experiment is 86.6% across 15 periods, which increases to 96.0% after period 5. Analyzing choice data and responses to the pre-play questionnaires reveals that subjects defect because of free-riding motivations or feelings of uncertainty in others’ cooperation. After observing defections, cooperators switch to defection, which decreases cooperation rates between the first and second stages of each period. |
| Keywords: | social dilemma, public good, experiment |
| JEL: | C72 C92 D74 H41 P43 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:kch:wpaper:sdes-2014-7&r=gth |
| By: | Messan Agbaglah (Département d'économique, Université de Sherbrooke) |
| Abstract: | This paper develops an extension of the recursive core to the setting of overlapping coalitions. We show that the cooperative game theoretical traditional way of separating a deviant coalition from the game played by the ones left behind is no more satisfactory. We therefore introduce a new paradigm with which we obtain the overlapping coalition structure core whose allocations are Pareto-efficient. |
| Keywords: | Overlapping coalitions, Cover function game, Recursive core, Residual game, Optimistic, Pessimistic, Efficiency. |
| JEL: | C70 C71 D71 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:shr:wpaper:14-07&r=gth |
| By: | Sonmez, Tayfun O. |
| Abstract: | Sprumont (1990) shows that the Shapley value (Shapley 1957) is population-monotonic (Thomson 1983) on the class of convex games (Shapley 1971). In this paper we study the population-monotonicity of the nucleolus (Schmeidler 1969). We show that the nucleolus is not population-monotonic on the class of convex games. Our main result is that the nucleolus is population-monotonic on a class of public good problems which is formalized in Litilechild and Owen (1973) under the name of airport games. We also provide a recursive formula for the nucleolus of the airport game. |
| Keywords: | Population-monotonicity, airport game |
| JEL: | C71 |
| Date: | 2014–09–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:58248&r=gth |
| By: | B. Evci |
| Abstract: | We know from Gale and Shapley (1962) that every Two-Sided Matching Game has a stable solution. It is also well-known that the number of stable matchings increases with the number of agents on both sides. In this paper, we propose two mechanisms, one of which is a variant of the other, to the marriage problem. Our original mechanism implements the full set of stable matchings for any preference profile. On the other hand, the variant mechanism parititons the domain of preference profiles into two; for one set, it implements the full set of stable matchings like the original mechanism and for the other, it ends up with a proper subset of the set of stable matchings. Besides, for some profiles with multi stability, it gives one of the optimal stable matchings. Namely, the second mechanism coincides either with the original mechanism or it is an improvement for one side; and in some profiles, the algortihm induces Gale and Shapley's algorithm for some profiles. Thus, it is a "middle" mechanism. |
| JEL: | C78 D78 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:bol:bodewp:wp973&r=gth |
| By: | Andersson , Tommy (Department of Economics, Lund University); Ehlers, Lars (CIREQ) |
| Abstract: | We consider envy-free and budget-balanced rules that are least manipulable with respect to agents counting or with respect to utility gains, and observe that for any profile of quasi-linear preferences, the outcome of any such least manipulable envy-free rule can be obtained via agent-k-linked allocations. Given this observation, we provide an algorithm for identifying agent-k-linked allocations. |
| Keywords: | least manipulable envy-free rules; algorithm |
| JEL: | C71 C78 D63 D71 D78 |
| Date: | 2014–10–15 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:lunewp:2014_035&r=gth |
| By: | Erik Ansink (VU University Amsterdam); Harold Houba (VU University Amsterdam) |
| Abstract: | We survey the economics of transboundary river water allocation, which emerged in the 1960s and has matured over the last decade due to increasing concerns over water scarcity and pollution. We outline the major approaches and pay specific attention to the strategic aspects of transboundary river water allocation. These strategic aspects are captured by employing game theory to assess the economics of transboundary river water allocation in a simple model of river sharing. This model allows us to show how conflict and cooperation over transboundary water resources may occur. It also allows us to pay specific attention to the efficiency, sustainability, and fairness of solutions to this model. We compare and contrast both cooperative and non-cooperative approaches and we relate their solutions to illustrative examples. |
| Keywords: | River sharing problem, River claims problem, Fairness, Efficiency, Sustainability, Water allocation agreement, Bargaining, Water trade, Sharing rules, Axiomatic approach |
| JEL: | C71 C73 D63 D74 F53 Q25 |
| Date: | 2014–10–06 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20140132&r=gth |
| By: | Meinhardt, Holger Ingmar |
| Abstract: | To determine correctly a non-convex pre-kernel for TU games with more than 4 players can be a challenge full of possible pitfalls, even to the experienced researcher. Parts of the pre-kernel can be easily overlooked. In this note we discuss a method to present the full shape of the pre-kernel for a permutation game as discussed by Solymosi (2014). By using the property in which the pre-kernel is located in the least core for permutation games, the least core can be covered by a small collection of payoff equivalence classes as identified by Meinhardt (2013d) to finally establish the correct shape of the pre-kernel. |
| Keywords: | Transferable Utility Game: Non-Convex Pre-Kernel: Pre-Kernel Catcher: Convex Analysis: Fenchel-Moreau Conjugation: Indirect Function |
| JEL: | C63 C71 D63 D74 |
| Date: | 2014–10–18 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:59365&r=gth |
| By: | Emara, Noha; Owens, David; Smith, John; Wilmer, Lisa |
| Abstract: | We examine whether the predictions of minimax in zero-sum games holds under highly incentivized conditions with highly informed informed decision makers. We examine data from 3455 National Football League (NFL) games from the 2000 season through the 2012 season. We categorize every relevant play as either a rush or a pass. We find that, despite the predictions of minimax, the pass-rush mix exhibits negative serial correlation. In other words, given the conditions of the play, teams employ an exploitable strategy in that play types alternate more frequently than implied by an independent stochastic process. We also find that the efficacy of plays are affected by previous actions and previous outcomes in a manner that is not consistent with minimax. Our analysis suggests that teams could profit from more clustered play selections, which switch play type less frequently. Our results are consistent with the explanation that teams excessively switch play types in order to not be perceived as predictable. |
| Keywords: | serial correlation, game theory, mixed strategies, matching pennies |
| JEL: | C72 C93 D03 |
| Date: | 2014–09–26 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:58907&r=gth |
| By: | Iván Arribas (ERI-CES, University of Valencia, Ivie); Amparo Urbano Salvador (ERI-CES, University of Valencia) |
| Abstract: | This paper focuses on oligopolistic markets in which indivisible goods are sold by multiproduct firms to a continuum of homogeneous buyers, with measure normalized to one, who have preferences over bundles of products. Our analysis contributes to the literature on private, delegated agency games with complete information, extending the insights by Chiesa and Denicolò (2009) to multiproduct markets with indivisibilities and where the agent's preferences need not be monotone. By analyzing a kind of extended contract schedules -mixed bundling prices- that discriminate on exclusivity, the paper shows that efficient equilibria always exist in such settings. There may also exist inefficient equilibria in which the agent chooses a suboptimal bundle and no principal has a profitable deviation inducing the agent to buy the surplus-maximizing bundle because of a coordination problem among the principals. Inefficient equilibria can be ruled out by either assuming that all firms are pricing unsold bundles at the same profit margin as the bundle sold at equilibrium, or imposing the solution concept of subgame perfect strong equilibrium, which requires the absence of profitable deviations by any subset of principals and the agent. We also provide a characterization of the equilibrium strategies. More specific results about the structure of equilibrium prices and payoffs for common agency outcomes are ofered when the social surplus function is monotone and either submodular or supermodular. |
| Keywords: | Multiproduct Price Competition, Delegated Agency Games, Mixed Bundling Prices, Subgame Perfect Nash Equilibrium, Strong Equilibrium |
| JEL: | C72 D21 D41 D43 L13 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:dbe:wpaper:0614&r=gth |
| By: | Salvador Barberà; Anke Geber |
| Abstract: | We provide characterizations of the set of outcomes that can be achieved by agenda manipulation for two prominent sequential voting procedures, the amendment and the successive procedure. Tournaments and super-majority voting with arbitrary quota q are special cases of the general sequential voting games we consider. We show that when using the same quota, both procedures are non-manipulable on the same set of preference profiles, and that the size of this set is maximized under simple majority. However, if the set of attainable outcomes is not single-valued, then the successive procedure is more vulnerable towards manipulation than the amendment procedure. We also show that there exists no quota which uniformly minimizes the scope of manipulation, once this becomes possible. |
| Keywords: | sequential voting, agendas, manipulation |
| JEL: | C72 D02 D71 D72 |
| Date: | 2014–08 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:782&r=gth |
| By: | Allred, Sarah; Duffy, Sean; Smith, John |
| Abstract: | We study the relationship between the cognitive load manipulation and strategic sophistication. The cognitive load manipulation is designed to reduce the subject's cognitive resources that are available for deliberation on a choice. In our experiment, subjects are placed under a high cognitive load (given a difficult number to remember) or a low cognitive load (given a number that is not difficult to remember). Subsequently, the subjects play a one-shot game then they are asked to recall the number. This procedure is repeated for various games. We find a nuanced and nonmonotonic relationship between cognitive load and strategic sophistication. This relationship is consistent with two effects. First, subjects under a high cognitive load tend to exhibit behavior consistent with the reduced ability to compute the optimal decision. Second, the cognitive load tends to affect the subject's perception of their relative standing in the distribution of the available cognitive resources. The net result of these two opposing effects depends on the strategic setting. Our experiment provides evidence on the literature that examines the relationship between measures of cognitive ability and strategic sophistication. |
| Keywords: | bounded rationality, experimental economics, working memory load, cognition, strategic sophistication, rational inattention |
| JEL: | C72 C91 |
| Date: | 2014–10–22 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:59441&r=gth |
| By: | Hu Lu (Applied Research and Analysis Directorate, Health Canada); Yuntong Wang (Department of Economics, University of Windsor) |
| Abstract: | This paper considers a trading problem on a network with incomplete information. We consider a simple water trading problem in which three agents are located in a linear order along a river. Upper stream agents can sell some amount of the water to their downstream but not the other way around. The middle agent can be both a seller and a buyer. Agents have private information on their utility of water, which we assume is non- linear. We ask if there is an efficient trading mechanism for the allocation of water. We show that if agents have highly asymmetric initial endowments of water, incentive-compatible, individually rational, budget-balanced mechanisms exist that are also ex-post efficient. |
| Keywords: | Network; Incomplete Information; Water Trading; Mechanism Design. |
| JEL: | C72 D82 |
| Date: | 2014–10–27 |
| URL: | http://d.repec.org/n?u=RePEc:wis:wpaper:1405&r=gth |
| By: | Tatsuyoshi Saijo (Kochi University of Technology); Yutaka Kobayashi (Kochi University of Technology) |
| Abstract: | Efficient allocations in common-pool resources cannot be accomplished when appropriators are selfish. In addition to this dilemma, using a linear approximation of best response functions at the Nash equilibrium in the common-pool resource environment, we find that the system of simultaneous difference equations is locally unstable if the number of appropriators is at least four. This result indicates that the equilibrium analysis might not capture the essence of the common-pool resource problem, but provides an answer to ``some unexplained pulsing behavior'' (Ostrom, Journal of Economic Behavior and Organization, vol. 61, no.2 [2006], p. 150) of each appropriator's labor input in common-pool resource experiments. |
| JEL: | C62 C72 C92 Q22 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:kch:wpaper:sdes-2014-5&r=gth |
| By: | Jan Christoph Schlegel |
| Abstract: | It is shown that a matching market with contracts may be embedded into a matching market with salaries under weaker assumptions on preferences than substitutability. In particular, the result applies to the recently studied problem of cadet-to-branch matching. As an application of the embedding result, a new class of mechanisms for matching markets with contracts is defined that generalize the firm-proposing deferred acceptance algorithm to the case where firms have unilaterally substitutable preferences. |
| Keywords: | Matching; Matching with contracts; Matching with salaries; Embedding; Substitutes; Unilateral substitutes; Bilateral substitutes |
| JEL: | C78 |
| Date: | 2014–08 |
| URL: | http://d.repec.org/n?u=RePEc:lau:crdeep:14.05&r=gth |
| By: | Saidman, Susan L.; Roth, Alvin E.; Sonmez, Tayfun; Unver, M. Utku; Delmonico, Francis L. |
| Abstract: | Background: To expand the opportunity for paired live donor kidney transplantation, computerized matching algorithms have been designed to identify maximal sets of compatible donor/recipient pairs from a registry of incompatible pairs submitted as candidates for transplantation. Methods: Demographic data of patients who had been evaluated for live donor kidney transplantation but found to be incompatible with their potential donor (because of ABO blood group or positive crossmatch) were submitted for computer analysis and matching. Data included ABO and HLA types of donor and recipient, %PRA and specificity of recipient alloantibody, donor/recipient relationship, and the reason the donor was incompatible. The data set used for the initial simulation included 29 patients with one donor each and 16 patients with multiple donors for a total of 45 patients and 68 donor/patient pairs. In addition, a simulation based on OPTN/SRTR data was used to further assess the practical importance of multiple exchange combinations. Results: If only exchanges involving two patient-donor pairs were allowed, a maximum of 8 patient-donor pairs in the data set could exchange kidneys. If 3-way exchanges were also allowed, a maximum of 11 pairs could exchange kidneys. Simulations with OPTN/SRTR data demonstrate that the increase in the number of potential transplants if 3-way exchanges are allowed is robust, and does not depend on the particular patients in our sample. Conclusions: A computerized matching protocol can be used to identify donor/recipient pairs from a registry of incompatible pairs who can potentially enter into donor exchanges that otherwise would not readily occur. |
| Keywords: | Kidney Exchange |
| JEL: | C78 |
| Date: | 2014–09–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:58247&r=gth |
| By: | Avidit Acharya; Edoardo Grillo |
| Abstract: | We model a situation in which two countries are involved in a dispute. The dispute can end in a peaceful settlement, or it can escalate to war. If it is common knowledge that the countries are strategically rational, then the only equilibrium outcome of the model is peace. If, on the other hand, each country believes that there is some chance that its adversary is a crazy type that always behaves aggressively, then even a strategically rational country may have an incentive to pretend to be crazy. This leads to war with positive probability. In addition to being qualitatively different from the existing literature, our model (i) enables a more tractable analysis of two-sided incomplete informa- tion, (ii) has a generically unique equilibrium prediction, and (iii) yields several new comparative statics results. For example, we analyze the effect of increas- ing the prior probability that the countries are crazy types, as well as the effect of changing the relative military strengths of the countries, on equilib- rium behavior. In studying these comparative statics, our model identifies two countervailing forces that arise when the prior probability that a country is crazy decreases: a reputation motive that promotes less aggressive behavior by that country, and a defense motive that promotes more aggressive behavior by the other country. |
| Keywords: | war, conflict, bargaining, reputation |
| JEL: | C7 F5 N4 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:cca:wpaper:356&r=gth |