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on Game Theory |
| By: | Rene van den Brink (Vrije Universiteit Amsterdam); Dinko Dimitrov (Saarland University); Agnieszka Rusinowska (Paris School of Economics) |
| Abstract: | We study the issue of assigning weights to players that identify winning coalitions in plurality voting democracies. For this, we consider plurality games which are simple games in partition function form such that in every partition there is at least one winning coalition. Such a game is said to be precisely supportive if it is possible to assign weights to players in such a way that a coalition being winning in a partition implies that the combined weight of its members is maximal over all coalitions in the partition. A plurality game is decisive if in every partition there is exactly one winning coalition. We show that decisive plurality games with at most four players, majority games with an arbitrary number of players, and almost symmetric decisive plurality games with an arbitrary number of players are precisely supportive. Complete characterizations of a partition's winning coalitions are provided as well. |
| Keywords: | plurality game, plurality voting, precise support, simple game in partition function form, winning coalition |
| JEL: | C71 D62 D72 |
| Date: | 2019–08–26 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20190062&r=all |
| By: | Bayer, Péter (university of grenoble alpes); Herings, P. Jean-Jacques (General Economics 1 (Micro)); Peeters, Ronald (university of otago, dunedin) |
| Abstract: | Economic agents with an increased sophistication sometimes use their advantage to exploit their more naive counterparts. In public goods games played on networks, such an agent will attempt to manipulate as many of his neighbors as possible to produce the public good. We study the exploitation of a myopic population by a single farsighted player in such games. We show the existence and payoff-uniqueness of optimal farsighted strategies in every network structure. In the long run, the farsighted player’s effects are only felt locally. A simple dependence-withdrawal strategy reaches the optimal outcome for every network if the starting state is unfavorable, and reaches it for every starting state if the farsighted player is linked to all opponents. We characterize the lower and upper bounds of long-run payoffs the farsighted player can attain in a given network and make comparative statics with respect to adding a new link. The farsighted player always benefits from linking to more opponents (sociability) and is always harmed by his neighbors linking to each other (jealousy). |
| Keywords: | networks, public goods, myopic and farsighted players |
| JEL: | C73 D85 H41 |
| Date: | 2019–08–29 |
| URL: | http://d.repec.org/n?u=RePEc:unm:umagsb:2019023&r=all |
| By: | Sheremeta, Roman |
| Abstract: | The attack and defense game is a game in which an attacker (a group of attackers) has an incentive to revise the status quo and a defender (a group of defenders) wants to protect it. The asymmetry in objectives creates incompatible interests and results in a mixed-strategy Nash equilibrium. However, this equilibrium could be heavily impacted by behavioral considerations. |
| Keywords: | contest, attack, defense, experiment |
| JEL: | C72 C91 D72 D74 |
| Date: | 2018–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:95747&r=all |
| By: | Ghidoni, Riccardo; Suetens, Sigrid |
| Abstract: | Sequentiality of moves in an infinitely repeated prisoner's dilemma does not change the conditions under which mutual cooperation can be supported in equilibrium as compared to simultaneous decision-making. The nature of the interaction is different, however, given that the second mover in a sequential-move game does not face strategic uncertainty. We study in an experiment whether sequentiality has an effect on cooperation rates. We find that with intermediate incentives to cooperate, sequentiality increases cooperation rates by around 40 percentage points, whereas with very low or high incentives to cooperate, cooperation rates are respectively very low or high in both settings. |
| Keywords: | Cooperation; Experiment; infinitely repeated game; sequential prisoner's dilemma; Strategic uncertainty |
| JEL: | C70 C90 D70 |
| Date: | 2019–06 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:13809&r=all |
| By: | Hsieh, Chih-Sheng; König, Michael; Liu, Xiaodong |
| Abstract: | This paper introduces a structural model for the coevolution of networks and behavior. The microfoundation of our model is a network game where agents adjust actions and network links in a stochastic best-response dynamics with a utility function allowing for both strategic externalities and unobserved heterogeneity. We show the network game admits a potential function and the coevolution process converges to a unique stationary distribution characterized by a Gibbs measure. To bypass the evaluation of the intractable normalizing constant in the Gibbs measure, we adopt the Double Metropolis-Hastings algorithm to sample from the posterior distribution of the structural parameters. To illustrate the empirical relevance of our structural model, we apply it to study R&D investment and collaboration decisions in the chemicals and pharmaceutical industry and find a positive knowledge spillover effect. Finally, our structural model provides a tractable framework for a long-run key player analysis. |
| Keywords: | Double Metropolis-Hastings algorithm; Key players; network interactions; R&D collaboration networks; stochastic best-response dynamics; strategic network formation; Unobserved heterogeneity |
| JEL: | C11 C31 C63 C73 L22 |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:13911&r=all |
| By: | Erhan Bayraktar; Xin Zhang |
| Abstract: | We analyze an $N+1$-player game and the corresponding mean field game with state space $\{0,1\}$. The transition rate of $j$-th player is the sum of his control $\alpha^j$ plus a minimum jumping rate $\eta$. Instead of working under monotonicity conditions, here we consider an anti-monotone running cost. We show that the mean field game equation may have multiple solutions if $\eta |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1908.06207&r=all |
| By: | Mukund Sundararajan; Amir Najmi |
| Abstract: | The Shapley value has become a popular method to attribute the prediction of a machine-learning model on an input to its base features. The Shapley value [1] is known to be the unique method that satisfies certain desirable properties, and this motivates its use. Unfortunately, despite this uniqueness result, there are a multiplicity of Shapley values used in explaining a model's prediction. This is because there are many ways to apply the Shapley value that differ in how they reference the model, the training data, and the explanation context. In this paper, we study an approach that applies the Shapley value to conditional expectations (CES) of sets of features (cf. [2]) that subsumes several prior approaches within a common framework. We provide the first algorithm for the general version of CES. We show that CES can result in counterintuitive attributions in theory and in practice (we study a diabetes prediction task); for instance, CES can assign non-zero attributions to features that are not referenced by the model. In contrast, we show that an approach called the Baseline Shapley (BS) does not exhibit counterintuitive attributions; we support this claim with a uniqueness (axiomatic) result. We show that BS is a special case of CES, and CES with an independent feature distribution coincides with a randomized version of BS. Thus, BS fits into the CES framework, but does not suffer from many of CES's deficiencies. |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1908.08474&r=all |
| By: | Subhasish M. Chowdhury (Department of Economics, University of Bath); Philip J. Grossman (Department of Economics, Monash University); Joo Young Jeon (Department of Economics, University of Reading) |
| Abstract: | Research on altruistic payoffs and the related payoff anticipation and related gender differences is limited. Using data from Chowdhury & Jeon (2014) who vary a common show-up fee and incentivize recipients to anticipate the amount given in a dictator game, we find that the show-up fee has a positive effect on dictator giving for both genders. While female dictators are more generous than males, male recipients anticipate higher amounts than the amount male dictators give. The show-up fee affects the social-type of female dictators, and the anticipation about dictator social-type by the male recipients. |
| Keywords: | dictator-game; altruism; anticipatory-belief; gender |
| JEL: | C91 D64 D84 J16 |
| Date: | 2019–08–26 |
| URL: | http://d.repec.org/n?u=RePEc:rdg:emxxdp:em-dp2019-13&r=all |
| By: | Josue Ortega |
| 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 > 2 it requires that one agent receives no cake. We show that a weaker version of this property recently suggested by Troyan and Morril, called non-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. Non-obvious manipulability explains why leftmost leaves is manipulated less often in practice than other proportional mechanisms. |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1908.02988&r=all |
| By: | Martimort, David |
| Abstract: | Two conflicting interest groups buy favors from a policy-maker. Influence is modeled as a common agency game with lobbyists proposing monetary contributions contingent on decisions. When the preferences of the group members are common knowledge, groups form efficiently and lobbying competition perfectly aggregates preferences. When those preferences are instead private information, free riding in collective action arises within groups. Free riding implies that the influence of a group is weakened and that lobbying competition imperfectly aggregates preferences. By softening lobbying competition, private information might also increase groups' payoffs and hurt the policy-maker. Importantly, the magnitudes of informational frictions within each group are jointly determined at equilibrium. We draw from these findings a number of implications for the organization of interest groups. |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:13843&r=all |
| By: | Armstrong, Mark; Vickers, John |
| Abstract: | We explore patterns of competitive interaction by studying mixed-strategy equilibrium pricing in oligopoly settings where consumers vary in the set of suppliers they consider for their purchase. In the case of "nested reach" we find equilibria, unlike those in existing models, in which price competition is segmented: small firms offer only low prices and large firms only offer high prices. We characterize equilibria in the three-firm case using correlation measures of competition between pairs of firms. We then contrast them with equilibria in the parallel model with capacity constraints. A theme of the analysis is how patterns of consumer consideration matter for competitive outcomes. |
| Keywords: | Bertrand-Edgeworth competition; Captive customers; Consideration sets; Mixed strategies; price dispersion |
| JEL: | D43 D83 L11 L13 L15 |
| Date: | 2019–06 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:13821&r=all |
| By: | Bolin, Kristian (Department of Economics, School of Business, Economics and Law, Göteborg University); Caputo, Michael R. (Department of Economics, University of Central Florida) |
| Abstract: | Investments in the human capital of children during their upbringing determine the opportunities available in adulthood. Recognizing that the parent-child interaction plays a significant role in the accumulation of child human capital, we develop a differential game in which the parent may invest directly in child human capital and the child consumes goods that influence the accumulation of their human capital. We compare the accumulation of child human capital between three different parenting styles, formalized as three different solution concepts to the differential game: (i) the parent and the child maximizes a joint utility function (cooperative solution), (ii) the parent announces a strategy dependent on time only (open-loop Stackelberg), (iii) the parent’s strategy depends on the accrued amount of human capital (feedback Stackelberg). We show that under rather general assumptions the open-loop Stackelberg equilibrium is time consistent, and coincides with a feedback Stackelberg equilibrium. Using cooperative parenting as a benchmark, we find that less or more child human capital may be accumulated over the family’s planning horizon under “open-loop Stackelberg” parenting, depending on parental and child preferences for human capital and wealth at the terminal time of the family’s planning horizon, and on the extent to which child consumption influences the accumulation of their human capital. In particular, if the child’s preference for terminal time wealth is strong enough, more human capital will be accumulated under “open-loop Stackelberg” parenting. |
| Keywords: | Differential Game Theory; Intertemporal Choice; Human Capital |
| JEL: | C73 J24 |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:gunwpe:0771&r=all |
| By: | Ritz, R. |
| Abstract: | How does market power affect the rate of pass-through from marginal cost to the market price? A standard intuition is that more competition makes prices more “cost-reflective” and thus raises cost pass-through. This paper shows that this intuition is sensitive to the common assumption in the literature that firms’ marginal costs are constant. If firms have even modestly increasing marginal costs, more intense competition actually reduces pass through. These results apply to the “normal” case where pass-through is less than 100%. They have implications for competition policy and environmental regulation. |
| Keywords: | Cost pass-through, imperfect competition, perfect competition, production technology |
| JEL: | D24 D41 D42 D43 |
| Date: | 2019–08–21 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1974&r=all |
| By: | Ryosuke Ishii; Kuninori Nakagawa |
| Abstract: | In this study, we consider research and development investment by the government. Our study is motivated by the bias in the budget allocation owing to the competitive funding system. In our model, each researcher presents research plans and expenses, and the government selects a research plan in two periods---before and after the government knows its favorite plan---and spends funds on the adopted program in each period. We demonstrate that, in a subgame perfect equilibrium, the government adopts equally as many active plans as possible. In an equilibrium, the selected plans are distributed proportionally. Thus, the investment in research projects is symmetric and unbiased. Our results imply that equally widespread expenditure across all research fields is better than the selection of and concentration in some specific fields. |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1908.08786&r=all |
| By: | Enrique Fatas (School of Business and Economics, Loughborough University); Joo Young Jeon (Department of Economics, University of Reading); Paloma Ubeda (School of Economics and Business, Universidad Nacional de Educación a Distancia) |
| Abstract: | We investigate experimentally the effects of various sources of rebates on charity donation. Subjects first play a repeated public good game (PGG) with either a low or a high endowment and then have an option to donate to a charity. They may receive a rebate on their donation either exogenously (from the experimenter) or endogenously (from the public account of the PGG), or a rebate might not be available. When the PGG endowment level is low, the endogenous rebate scheme has a negative effect on charity giving. The exogenous rebate scheme, however, does not have any such effect. If the endowment level is high and the rebate is endogenous, then other-regarding preferences become salient and boost up charity donation. Females donate more than males, but only under the endogenous rebate scheme. These results shed light on the effects of the rebate schemes on different income and demographic factors, and provide with relevant policy implications. |
| Keywords: | donation; rebate; dictator game; public good game |
| JEL: | C91 C92 D64 |
| Date: | 2019–08–26 |
| URL: | http://d.repec.org/n?u=RePEc:rdg:emxxdp:em-dp2019-12&r=all |