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on Game Theory |
| By: | Marco Pelliccia (Department of Economics, Mathematics & Statistics, Birkbeck) |
| Abstract: | We study a Rubinstein-Stahl two-player non-cooperative bargaining game played by n players connected in a communication network. We allow the players to communicate with any peer in the same component via the existing paths connecting the peers in a given communication network (global interaction). The unique stationary subgame perfect equilibrium profile characterizes the players’ expected payoff as function of their betweenness centrality score. Secondly, we study a dynamic link-formation game which allows the players to activate new linkages or sever existing ones in order to increase their bargaining power for a given marginal cost per link. We identify the conditions under which the pairwise stable network structures which arise belong to the family of the nested split graphs. These are graphs where the neighbourhood of each node is contained in the neighbourhoods of nodes with higher degrees. |
| Keywords: | Communication; Network; Noncooperative bargaining; Network formation. |
| JEL: | C72 C78 D85 |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:bbk:bbkefp:1507&r=gth |
| By: | Sudhölter, Peter (Department of Business and Economics); Zarzuelo, José M. (Faculty of Economics and Business Administration) |
| Abstract: | A highway problem is a cost sharing problem that arises if the common resource is an ordered set of sections with fixed costs such that each agent demands consecutive sections. We show that the core, the prenucleolus, and the Shapley value on the class of TU games associated with highway problems possess characterizations related to traditional axiomatizations of the solutions on certain classes of games. However, in the formulation of the employed simple and intuitive properties the associated games do not occur. The main axioms for the core and the nucleolus are consistency properties based on the reduced highway problem that arises from the original highway problem by eliminating any agent of a specific type and using her charge to maintain a certain part of her sections. The Shapley value is characterized with the help of individual independence of outside changes, a property that requires the fee of an agent only depending on the highway problem when truncated to the sections she demands. An alternative characterization is based on the new contraction property. Finally it is shown that the games that are associated with generalized highway problems in which agents may demand non-connected parts are the positive cost games, i.e., nonnegative linear combinations of dual unanimity games. |
| Keywords: | TU game; airport problem; highway problem; core; nucleolus; Shapley value |
| JEL: | C71 |
| Date: | 2015–07–07 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:sdueko:2015_013&r=gth |
| By: | Mikhail Freer (Interdisciplinary Center for Economic Science and Department of Economics, George Mason University); Mariia Titova (National Research University Higher School of Economics, Moscow, Russia) |
| Abstract: | In this paper, we present a solution to the many-to-many matching problem with quotas. In our setting, we have students who select an exact number of courses (exact quota qs), and courses that must admit at least qc students (lower quota). We present a generalization of the deferred acceptance mechanism introduced in Gale and Shapley (1962), which returns the best pairwise-stable matching for courses, which is also uniform: every course has approximately the same number of students.Length: 7 |
| Keywords: | two-sided matching, stability |
| Date: | 2015–02 |
| URL: | http://d.repec.org/n?u=RePEc:gms:wpaper:1052&r=gth |
| By: | Lopez Maria Claudia (Department of Community Sustainability, Michigan State University, MI USA); Munro Alistair (GRIPS); Tarazona-Gomez Marcela (Oxford Policy Management, United Kingdom) |
| Abstract: | A recurring and puzzling pattern with experiments on intra-household behaviour is the common failure of couples to attain the cooperative solution. Using married couples from a low income area of Bogota, Colombia we conduct an experiment that raises the salience of the family vis-à-vis outsiders. In this experiment husbands and wives play a repeated voluntary contribution game. At the same time each participant plays an identical game with one stranger in the same session. When investments to the common pools are made from separate and non-fungible budgets, most subjects contribute more to the household pool than the stranger pool, but rarely contribute everything to the household even after repetition and opportunities for learning. Efficiency is not obtained. However, when subjects make contributions to the two games from a single budget many individuals converge rapidly on a strategy of investing everything in the household pool and contributing little to the pool with a stranger. Overall the amount invested in some pool rises. Our results are in line with games played with individuals in which in-group cooperation is higher when membership of the group is more salient. They suggest that strengthening family identity may raise intrahousehold cooperation, but at the expense of cooperation of interhousehold cooperation. |
| Date: | 2015–07 |
| URL: | http://d.repec.org/n?u=RePEc:ngi:dpaper:15-10&r=gth |
| By: | Kota Murayama (Department of Economics, Northwestern University, USA) |
| Abstract: | When players have a finite depth of reasoning, it is usually assumed that each player has a commonly known anchor behavior. This paper provides a general framework to examine whether predictions are robust to uncertainty about other players' anchors. We give two different sufficient conditions for the robustness. The first condition shows that any p-dominant equilibrium is robust if players put sufficiently small probability (decreasing in p) on high-depth types. This result highlights a distinction between two prominent finite depth of reasoning models: a risk dominated equilibrium is robust in the cognitive hierarchy model, but not in the level-k model. We also show that equilibria of dominance solvable models are robust. |
| Keywords: | Robustness, Iterative reasoning, Level-k model, Cognitive-hierarchy model, Higher-order belief, Bounded rationality |
| Date: | 2015–07 |
| URL: | http://d.repec.org/n?u=RePEc:kob:dpaper:dp2015-28&r=gth |
| By: | Mitra, Manipushpak; De, Parikshit |
| Abstract: | We address the mechanism design issue for the sequencing problem. We identify the just sequencing rule that serves the agents in the non-increasing order of their waiting costs and prove that it is a Rawlsian rule. We identify all rVCG mechanisms that implement the just sequencing rule. The other properties of the just sequencing rule that we identify are the following. It is an affine cost minimizer. It can be implemented with budget balanced rVCG mechanisms. Finally, when waiting cost and processing time are private information, we identify all generalized rVCG mechanisms that ex-post implement the just sequencing rule. |
| Keywords: | sequencing, implementation, outcome efficient sequencing rule, just sequencing rule, budget balance, ex-post implementation. |
| JEL: | C72 D63 D82 |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:65447&r=gth |
| By: | Michel Grabisch (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics) |
| Abstract: | The paper studies the vector space of set functions on a finite set X, which can be alternatively seen as pseudo-Boolean functions, and including as a special cases games. We present several bases (unanimity games, Walsh and parity functions) and make an emphasis on the Fourier transform. Then we establish the basic duality between bases and invertible linear transform (e.g., the Möbius transform, the Fourier transform and interaction transforms). We apply it to solve the well-known inverse problem in cooperative game theory (find all games with same Shapley value), and to find various equivalent expressions of the Choquet integral. |
| Abstract: | Nous étudions l'espace vectoriel des fonctions d'ensemble sur un espace fini X, qui peuvent être vues aussi comme des fonctions pseudo-booléennes, et incluent comme cas particulier les jeux. Nous présentons plusieurs bases (jeux unanimes, fonctions de Walsh, fonctions de parité) ainsi que la transformée de Fourier. Nous établissons la dualité fondamentale entre les bases et les transformées linéaires et inversibles (e.g., la transformée de Möbius, de Fourier et les transformées en interaction). Nous l'appliquons pour résoudre le problème inverse bien connu de la théorie des jeux coopératifs (trouver tous les jeux ayant la même valeur de Shapley), et pour trouver différentes expressions équivalentes pour l'intégrale de Choquet. |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-01169287&r=gth |
| By: | Ulrich Faigle (Universität zu Köln - Mathematisches Institut); Michel Grabisch (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics) |
| Abstract: | The problem of least square approximation for set functions by set functions satisfying specified linear equality or inequality constraints is considered. The problem has important applications in the field of pseudo-Boolean functions, decision making and in cooperative game theory, where approximation by additive set functions yields so-called least square values. In fact, it is seem that every linear value for cooperative games arises from least square approximation. We provide a general approach and problem overview. In particular, we derive explicit formulas for solutions under mild constraints, which include and extend previous results in the literature. |
| Abstract: | On considère le problème de l'approximation au sens des moindres carrés des fonctions d'ensemble par des fonctions d'ensemble satisfaisant des contraintes linéaires d'égalité ou d'inégalité. Le problème a des applications importantes dans le domaine des fonctions pseudo-Booléennes, la décision et la théorie des jeux coopératifs, où l'approximation par des jeux additifs mène à la notion de valeur aux moindres carrés. En fait, on voit que toute valeur linéaire pour les jeux coopératifs vient d'un problème d'approximation par les moindres carrés. Nous proposons une approche générale du problème. En particulier, nous obtenons des formules explicites pour les solutions sous des hypothèses faibles, qui incluent et étendent des résultats précédents de la littérature. |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-01169281&r=gth |
| By: | Marco Pelliccia (Department of Economics, Mathematics & Statistics, Birkbeck) |
| Abstract: | We model the decentralised defence choice of agents connected in a directed graph and exposed to an external threat. The network allows the players to receive goods from one or more producers through directed paths. Each agent is endowed with a finite and divisible defence resource that can be allocated to their own security or to that of their peers. The external threat is represented by an intelligent attacker who aims to maximise the flow-disruption by seeking to destroy one node. The set of the attacker’s potential targets is a subset of the set of middleman nodes and producers. These are the critical nodes with highest brokerage power in a directed network and therefore crucial to the system-flow. We show that a decentralised defence allocation is efficient when we assume perfect information: a centralised allocation of defence resources which minimises the flow-disruption coincides with a decentralised allocation. On the other hand, when we assume imperfect information, the decentralised allocation is inefficient and involves no reallocation of defence resources between the nodes. Finally, for a given connected graph, by increasing the link-density we can reduce the set of middleman nodes and thus the number of the potential targets. This also decreases the probability of a successful attack. |
| Keywords: | Networks; Network defence, Security. |
| JEL: | C69 |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:bbk:bbkefp:1506&r=gth |
| By: | Han, Jungsuk (Stockholm School of Economics); Sangiorgi, Francesco (Stockholm School of Economics) |
| Abstract: | This paper provides a microfounded information acquisition technology based on a simple framework with information search. When searchable information is limited, an agent encounters increasingly more redundant information in his search for new information. Redundancy slows down the learning process and generates decreasing returns. Further- more, as multiple agents search for information from the same source, limited searchabil- ity leads to covariance as the acquired information becomes increasingly more overlapped among agents. Using an asymptotic approach, we construct a tractable mapping from resource (attention) allocations to the precision and the correlation of agents’information under varying degrees of searchability of information. We study two economic applica- tions with endogenous information acquisition using our model: (i) a “beauty contest” coordination game, and (ii) a noisy rational expectations equilibrium. |
| Keywords: | information processing; concavity; precision; asymptotic analysis; coordina- tion games; portfolio choice; …nancial equilibrium |
| JEL: | C65 D80 D81 D83 G11 G14 |
| Date: | 2015–05–01 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:rbnkwp:0300&r=gth |
| By: | Guillen, Pablo.; Hakimov, Rustamdjan. |
| Abstract: | We run a field experiment to test the truth-telling rates of the theoretically strategy-proof Top Trading Cycles mechanism (TTC) under different information conditions. First, we asked first-year economics students enrolled in an introductory microeconomics unit about which topic, among three, they would most like to write an essay about. Most students chose the same favorite topic. Then we used TTC to distribute students equally across the three options. We ran three treatments varying the information the students received about the mechanism. In the first treatment students were given a description of the matching mechanism. In the second they received a description of the strategy-proofness of the mechanism without details of the mechanism. Finally, in the third they were given both pieces of information. We find a significant and positive effect of describing the strategy-proofness on truth-telling rates. ON the other hand, describing the matching mechanism has a significant and negative effect on truth-telling rates. |
| Date: | 2015–07 |
| URL: | http://d.repec.org/n?u=RePEc:syd:wpaper:2015-16.&r=gth |
| By: | Johanna Mollerstrom (Interdisciplinary Center for Economic Science and Department of Economics, George Mason University); Bjørn-Atle Reme (Telenor Research and NHH Norwegian School of Economics); Erik Ø. Sørensen (NHH Norwegian School of Economics) |
| Abstract: | We conduct a laboratory experiment where third-party spectators can re- distribute resources between two agents, thereby offsetting the consequences of controllable and uncontrollable luck. Some spectators go to the limits and equalize all or no inequalities, but many follow an interior allocation rule previously unaccounted for by the fairness views in the literature. These interior allocators regard an agent’s choice as more important than the cause of her low income and do not always compensate bad un- controllable luck. Instead, they condition such compensation on the agent’s decision regarding controllable luck exposure, even though the two types of luck are independent. Length: 33 |
| Keywords: | fairness, responsibility, option luck, brute luck, experiment |
| JEL: | C91 D63 D81 H23 |
| Date: | 2015–01 |
| URL: | http://d.repec.org/n?u=RePEc:gms:wpaper:1051&r=gth |
| By: | Rong Rong (Department of Economics, Weber State University); Daniel Houser (Interdisciplinary Center for Economic Science and Department of Economics, George Mason University) |
| Abstract: | Innovation occurs in network environments. Identifying the important players in the innovative  process,  namely  “the  innovatorsâ€,  is  key to understanding the process of innovation. Doing this requires flexible analysis tools tailored to work well with complex datasets generated within such environments. One such tool, cluster analysis, organizes a large data set into discrete groups based on patterns of similarity. It can be used to discover data patterns in networks without requiring strong ex ante assumptions about the properties of either the data generating process or the environment. This paper reviews key procedures and algorithms related to cluster analysis. Further, it demonstrates how to choose among these methods to identify the characteristics of players in a network experiment where innovation emerges endogenously. Length: 30 |
| Keywords: | cluster analysis, k-means algorithm, innovation, networks, laboratory experiment |
| JEL: | C46 C81 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:gms:wpaper:1049&r=gth |