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on Game Theory |
| By: | Michel Grabisch (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | It is known that for supermodular TU-games, the vertices of the core are the marginal vectors, and this result remains true for games where the set of feasible coalitions is a distributive lattice. Such games are induced by a hierarchy (partial order) on players. We propose a larger class of vertices for games on distributive lattices, called min-max vertices, obtained by minimizing or maximizing in a given order the coordinates of a core element. We give a simple formula which does not need to solve an optimization problem to compute these vertices, valid for connected hierarchies and for the general case under some restrictions. We find under which conditions two different orders induce the same vertex for every game, and show that there exist balanced games whose core has vertices which are not min-max vertices if and only if n > 4. |
| Keywords: | vertex,TU games,restricted cooperation,game with precedence constraints,core |
| Date: | 2018–03 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:hal-02043275&r=all |
| By: | Marco Battaglini (Cornell University and EIEF) |
| Abstract: | We propose a new model of legislative bargaining in which coalitions have different values, reflecting the fact that the policies they can pursue are constrained by the identity of the coalition members. In the model, a formateur picks a coalition and negotiates for the allocation of the surplus it is expected to generate. The formateur is free to change coalitions to seek better deals with other coalitions, but she may lose her status if bargaining breaks down, in which case a new formateur is chosen. We show that as the delay between offers goes to zero, the equilibrium allocation converges to a generalized version of a Nash Bargaining Solution in which — in contrast to the standard solution — the coalition is endogenous and determined by the relative coalitional values. A form of the hold-up problem specific to these bargaining games may lead to significant inefficiencies in the selection of the equilibrium coalition. We use the equilibrium characterization of the distortions to study the role of the head of state in avoiding (or containing) distortions. We also show that the model helps rationalizing well known empirical facts that are in conflict with the predictions of standard non-cooperative models of bargaining: the absence of significant (or even positive) premia in ministerial allocations for formateurs and their parties;the occurrence of supermajorities;and delays in reaching agreements. |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:eie:wpaper:1902&r=all |
| By: | Mallozzi, Lina; Vidal-Puga, Juan |
| Abstract: | We study cooperative interval games. These are cooperative games where the value of a coalition is given by a closed real interval specifying a lower bound and an upper bound of the possible outcome. For interval cooperative games, several (interval) solution concepts have been introduced in the literature. We assume that each player has a different attitude towards uncertainty by means of the so-called Hurwicz coefficients. These coefficients specify the degree of optimism that each player has, so that an interval becomes a specific payoff. We show that a classical cooperative game arises when applying the Hurwicz criterion to each interval game. On the other hand, the same Hurwicz criterion can be also applied to any interval solution of the interval cooperative game. Given this, we say that a solution concept is Hurwicz compatible if the two procedures provide the same final payoff allocation. When such compatibility is possible, we characterize the class of compatible solutions, which reduces to the egalitarian solution when symmetry is required. The Shapley value and the core solution cases are also discussed. |
| Keywords: | Cooperative interval games; Hurwicz criterion; Hurwicz compatibility |
| JEL: | C71 |
| Date: | 2019–03–12 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:92730&r=all |
| By: | Dan Kovenock (Economic Science Institute, Chapman University); David Rojo Arjona (Chapman University) |
| Abstract: | We fully characterize best-response functions in Colonel Blotto games with lottery contest success functions. |
| Keywords: | Multi-Battle contest, Colonel Blotto game, Contest success function, Best-response, Conflict |
| JEL: | C61 C72 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:19-05&r=all |
| By: | Besner, Manfred |
| Abstract: | We present new axiomatic characterizations of five classes of TU-values, the classes of the weighted, positively weighted, and multiweighted Shapley values, random order values, and the Harsanyi set. The axiomatizations are given in parallel, i.e., they differ only in one axiom. In conjunction with marginality, a new property, called coalitional differential dependence, is the key that allows us to dispense with additivity. In addition, we propose new axiomatizations of the above five classes, in which, in part new, different versions of monotonicity, associated with the strong monotonicity in Young (1985), are decisive. |
| Keywords: | Cooperative game; Marginality; Strong monotonicity; Coalitional differential dependence; Weighted Shapley values · Harsanyi set |
| JEL: | C7 C71 |
| Date: | 2019–03–15 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:92771&r=all |
| By: | Bergantiños, Gustavo; Gómez-Rúa, María; Llorca, Natividad; Pulido, Manuel; Sánchez-Soriano, Joaquin |
| Abstract: | This paper deals with the problem of allocating costs in set covering situations. In particular, we focus on set covering situations where the optimal covering is given in advance. Thus, we take into account only the facilities that have to be opened and look for rules distributing their cost. We define a cooperative game and study the core and the nucleolus. We also introduce two new rules: the equal split rule on facilities and the serial rule. We axiomatically characterize the core, the nucleolus, and the two rules. Finally, we study several monotonicity properties of the rules. |
| Keywords: | set covering problems; cost sharing rules; cooperative games |
| JEL: | C71 |
| Date: | 2019–03–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:92659&r=all |
| By: | Nakagawa, Shintaro |
| Abstract: | Cornes and Itaya (2010) showed that in a two-player game of voluntary provision of two public goods if the players have different preferences, and if both players simultaneously make positive contributions to both public goods, the system of equations representing the Nash equilibrium is overdetermined. We extend this proposition to a model of voluntary provision of two or more public goods and show that if the players have different preferences, and if the number of players who contribute simultaneously to two or more public goods is more than the number of public goods, the system representing the Nash equilibrium is overdetermined. This result implies that in a large group, the share of players contributing to multiple public goods may well be quite small and the majority of the players may contribute to at the most one public good. |
| Keywords: | Voluntary provision; multiple public goods |
| JEL: | H41 |
| Date: | 2019–03–15 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:92719&r=all |
| By: | Güth, Werner; Stadler, Manfred; Zaby, Alexandra |
| Abstract: | In capacity-then-price-setting games, soft capacity constraints are planned sales amounts where producing above capacity is possible but more costly. While the subgame perfect equilibrium predicts equal prices, experimental evidence often reveals price discrepancies. This failure to coordinate on equal prices can imply losses, especially when serving demand is obligatory. We compare coordination failure with efficient rationing as well as with compulsory serving of demand, and additionally allow for simultaneous and sequential capacity choices. These treatments lead to a varying severity of the threat of losses. Our experimental results show that (possible) coordination failure affects behavior through two channels: via anticipating as well as via reacting to a loss. While capacities increase in anticipation of losses, prices increase when anticipating losses but decrease after experiencing losses. Coordination failures are more probable after subjects experienced a loss. |
| Keywords: | capacity-then-price competition,loss avoidance,path dependence,sequentiality of decisions,intra-play communication |
| JEL: | C72 C91 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:tuewef:116&r=all |
| By: | Baogui Xin; Wei Peng; Yekyung Kwon |
| Abstract: | We reconsider the Cournot duopoly problem in light of the theory for long memory. We introduce the Caputo fractional-order difference calculus to classical duopoly theory to propose a fractional-order discrete Cournot duopoly game model, which allows participants to make decisions while making full use of their historical information. Then we discuss Nash equilibria and local stability by using linear approximation. Finally, we detect the chaos of the model by employing a 0-1 test algorithm. |
| Date: | 2019–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1903.04305&r=all |
| By: | Hamamura, Jumpei |
| Abstract: | This study analytically investigates the choice of a cost accounting system based on the cost-based transfer price by a divisionalized firm that has a direct channel through electronic commerce (EC). The findings show that the optimal choice between direct and absorption costing affects the increase of overhead allocation for the retail division through the cost-based transfer price. While traditional strategic transfer pricing literature shows that absorption costing is optimal in specific economic environments, this study demonstrates that direct costing is also optimal in a specific economic environment by considering dual channel competition. This research thus contributes to the extant strategic transfer pricing literature, which considers the choice of a cost accounting system in management accounting. |
| Keywords: | Economics; Game theory; Cost-based transfer pricing; Cost accounting; Direct channel |
| JEL: | D43 M41 |
| Date: | 2018–12–25 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:92643&r=all |
| By: | Sarfati, M.; Hesamzadeh, M-R.; Holmberg, P. |
| Abstract: | Electricity markets employ different congestion management methods to handle the limited transmission capacity of the power system. This paper compares production efficiency and other aspects of nodal and zonal pricing. We consider two types of zonal pricing: zonal pricing with Available Transmission Capacity (ATC) and zonal pricing with Flow-Based Market Coupling (FBMC).We develop a mathematical model to study the imperfect competition under zonal pricing with FBMC. Zonal pricing with FBMC is employed in two stages, a day-ahead market stage and a re-dispatch stage. We show that the optimality conditions and market clearing conditions can be reformulated as a mixed integer linear program (MILP), which is straightforward to implement. Zonal pricing with ATC and nodal pricing is used as our benchmarks. The imperfect competition under zonal pricing with ATC and nodal pricing are also formulated as MILP models. All MILP models are demonstrated on 6-node and the modified IEEE 24-node systems. Our numerical results show that the zonal pricing with ATC results in large production inefficiencies due to the incdec-game. Improving the representation of the transmission network as in the zonal pricing with FBMC mitigates the inc-dec game. |
| Keywords: | Congestion management, Zonal pricing, Flow-based market coupling |
| JEL: | C61 C72 D43 L13 L94 |
| Date: | 2019–02–27 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1919&r=all |
| By: | Joseph, Andreas (Bank of England) |
| Abstract: | Machine learning models often excel in the accuracy of their predictions but are opaque due to their non-linear and non-parametric structure. This makes statistical inference challenging and disqualifies them from many applications where model interpretability is crucial. This paper proposes the Shapley regression framework as an approach for statistical inference on non-linear or non-parametric models. Inference is performed based on the Shapley value decomposition of a model, a pay-off concept from cooperative game theory. I show that universal approximators from machine learning are estimation consistent and introduce hypothesis tests for individual variable contributions, model bias and parametric functional forms. The inference properties of state-of-the-art machine learning models — like artificial neural networks, support vector machines and random forests — are investigated using numerical simulations and real-world data. The proposed framework is unique in the sense that it is identical to the conventional case of statistical inference on a linear model if the model is linear in parameters. This makes it a well-motivated extension to more general models and strengthens the case for the use of machine learning to inform decisions. |
| Keywords: | Machine learning; statistical inference; Shapley values; numerical simulations; macroeconomics; time series |
| JEL: | C45 C52 C71 E47 |
| Date: | 2019–03–08 |
| URL: | http://d.repec.org/n?u=RePEc:boe:boeewp:0784&r=all |
| By: | Nagy, Balázs; Tasnádi, Attila |
| Abstract: | The government may regulate a market by obtaining partial ownership in a firm. This type of socially concerned firm behaves as a combined profit and social surplus maximizer. We investigate the presence of a socially concerned firm in the framework of a Bertrand-Edgeworth duopoly with capacity constraints. In particular, we determine the mixed-strategy equilibrium of this game and relate it to both the standard and the mixed versions of the Bertrand-Edgeworth game. In contrast to other results in the literature we find that full privatization is the socially best outcome, that is the optimal level of public ownership is equal to zero. |
| Keywords: | Bertrand-Edgeworth, mixed duopoly, semi-public firm, mixedstrategy equilibrium |
| JEL: | D43 L13 |
| Date: | 2019–02–28 |
| URL: | http://d.repec.org/n?u=RePEc:cvh:coecwp:2019/03&r=all |
| By: | Katinka Kristine Holtsmark; Kristoffer Midttømme |
| Abstract: | This paper presents a novel benefit of linking emission permit markets. We let countries issue permits non-cooperatively, and with endogenous technology we show there are gains from permit trade even if countries are identical. Linking the permit markets of different countries will turn permit issuance into intertemporal strategic complements. The intertemporal strategic complementarity arises because issuing fewer permits today increases investments in green energy capacity in all permit market countries, and countries with a higher green energy capacity will respond by issuing fewer permits in the future. Hence, each country faces incentives to withhold emission permits when permit markets are linked. Even though countries cannot commit to reducing their own emissions, or punish other countries that do not, the outcome is reduced emissions, higher investments, and increased welfare, compared to a benchmark with only domestic permit trade. We also show that permit market linking can arise as an equilibrium outcome. |
| Keywords: | international agreements, permit markets, dynamic games, green technology investments |
| JEL: | F55 Q54 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_7548&r=all |
| By: | Adriana Breaban (Chapman University and Erasmus University of Rotterdam); Charles N. Noussair (University of Arizona); Andreea Victoria Popescu (Tilburg University) |
| Abstract: | Competition for a prize frequently takes the form of dedicating time toward winning a contest. Those who spend the most time become more likely to obtain the prize. We model this competition as an all-pay auction under incomplete information, and report an experiment in which expenditures and rewards are in terms of time. In the experiment, subjects must stay in the laboratory doing nothing for an initially prespecified length of time. However, they can bid, in terms of time, to leave early. The auction has an allpay structure so that if an individual does not submit the highest bid within her group, she must stay for the additional time that she bid. We correlate behavior in this game with behavior in an isomorphic all-pay auction played with money bids. We also consider how two measures of sophistication, the Cognitive Reflection Test (CRT) score, and performance on a probability calibration task, correlate with behavior. We find strong similarities in overall behavior between the auctions conducted with money and with time. Bidding greater than equilibrium levels is typical, and as a consequence, average earnings are negative in both auctions. Thus, the result that there is overdissipation of rent in all-pay auctions extends to competition in terms of time. Higher CRT score and more accurate probability calibration correlate with better decisions in auctions played for money but not those played for time. |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:18-20&r=all |
| By: | Barron, Kai; Huck, Steffen; Jehiel, Philippe |
| Abstract: | In this paper, we design an investment game which allows us to study the influence of selection when learning from others. Using the theoretical study of selection neglect in Jehiel (2018) as a guide, we test (i) for the presence of selection neglect in this investment context, and (ii) some comparative static predictions of the model. We find strong evidence for selection neglect—even though subjects are fully informed about the data generating process. As theoretically predicted, the degree of bias due to selection neglect increases when other decision makers become more informed, or become more rational. It decreases when signals are correlated. |
| Keywords: | selection neglect,beliefs,overconfidence,experiment,survivorship bias,bounded rationality |
| JEL: | C11 C90 D80 D83 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:wzbeoc:spii2019301&r=all |
| By: | Toomas Hinnosaar |
| Abstract: | The standard model of sequential capacity choices is the Stackelberg quantity leadership model with linear demand. I show that under the standard assumptions, leaders' actions are informative about market conditions and independent of leaders' beliefs about the arrivals of followers. However, this Stackelberg independence property relies on all standard assumptions being satisfied. It fails to hold whenever the demand function is non-linear, marginal cost is not constant, goods are differentiated, firms are non-identical, or there are any externalities. I show that small deviations from the linear demand assumption may make the leaders' choices completely uninformative. |
| Date: | 2019–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1903.04060&r=all |
| By: | Hélia Marreiros (Universidade Católica Portuguesa, Católica Porto Business School and CEGE) |
| Abstract: | We experimentally investigate the welfare implications of two distinct output sharing rules in partnerships with a heterogeneous composition. In particular the paper examines the tradeoff between the potential benefits of a simple equal output sharing rule and a distribution rule that maximizes total welfare, the second best sharing rule. This output sharing rule, which is recommended, is unequal in heterogeneous production groups. The experimental setup is based on a team production technology model, where Nash equilibrium contributions are located in the interior of the set of feasible contributions. The results confirm that second best output sharing rules give higher welfare than equal ones when the two are different. Then, there is a trade off to be considered, when deciding on the team composition (the equal sharing rule is second best optimal in homogeneous partnerships), and when deciding the sharing rule given the group composition. We also find that the experimentally created wealth with equal sharing is higher than the anticipated from pure rational behavior because less skilled collaborating partners contribute with more input than anticipated. This is interpreted as evidence that less productive partners perceive a sense of unfairness when receive a similar share of output than the more productive ones, and decide to correspond with higher input contribution. |
| Keywords: | PPartnerships; Team Production, Incentives; Efficiency; Equality; Experiment |
| JEL: | C92 D63 J33 M52 |
| Date: | 2019–01 |
| URL: | http://d.repec.org/n?u=RePEc:cap:wpaper:012019&r=all |
| By: | Michalis Drouvelis; Nikolaos Georgantzis |
| Abstract: | Many modern organisations collect data on individuals’ personality traits as part of their human resource selection processes. We test experimentally whether revealing information on personality data impacts on pro-social behaviour as measured in a one-shot modified dictator game and a public goods game. Our focus is on the personality trait of agreeableness which has been shown to be a significant determinant of pro-sociality. We provide new evidence that revealing personality information for disagreeable individuals has detrimental effects on their pro-social behaviour as compared to the baseline no-information benchmark. This is not the case, however, for agreeable individuals when they are matched with agreeable individuals. Agreeable individuals become less pro-social when matched with disagreeable individuals and are aware of this. Our results suggest that information cues about personality significantly affect economic behaviour and have implications for employees’ personality assessments as part of standard hiring processes. |
| Keywords: | personality, social preferences, inequity aversion, cooperation, laboratory experiment |
| JEL: | C91 D70 H41 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_7538&r=all |