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on Game Theory |
| By: | Christian Ewerhart |
| Abstract: | While smooth exact potential games are easily characterized in terms of the cross-derivatives of players' payoff functions, an analogous differentiable characterization of ordinal or generalized ordinal potential games has been elusive for a long time. In this paper, it is shown that the existence of a generalized ordinal potential in a smooth game with multi-dimensional strategy spaces is crucially linked to the semipositivity (Fiedler and Ptak, 1966) of a modified Jacobian matrix on the set of interior strategy profiles at which at least two first-order conditions hold. Our findings imply, in particular, that any generalized ordinal potential game must exhibit pairwise strategic complements or substitutes at any interior Cournot-Nash equilibrium. Moreover, provided that there are more than two players, the cross-derivatives at any interior equilibrium must satisfy a rather stringent equality constraint. The two conditions, which may be conveniently condensed into a local variant of the differentiable condition for weighted potential games, are made explicit for sum-aggregative games, symmetric games, and two-person zero-sum games. For the purpose of illustration, the results are applied to classic games, including probabilistic all-pay contests with heterogeneous valuations, models of mixed oligopoly, and Cournot games with a dominant firm. |
| Keywords: | Ordinal potentials, smooth games, strategic complements and substitutes, semipositive matrices |
| JEL: | C6 C72 D43 D72 |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:265&r=gth |
| By: | Elon Kohlberg; Abraham Neyman |
| Abstract: | A game of threats on a finite set of players, $N$, is a function $d$ that assigns a real number to any coalition, $S \subseteq N$, such that $d \left( S \right) = - d \left( N \setminus S \right)$. A game of threats is not necessarily a coalitional game as it may fail to satisfy the condition $d \left( \emptyset \right) = 0$. We show that analogs of the classic Shapley axioms for coaltional games determine a unique value for games of threats. This value assigns to each player an average of the threat powers, $d \left( S \right)$, of the coalitions that include the player. |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp710&r=gth |
| By: | Florian Engl; Arno Riedl; Roberto A. Weber |
| Abstract: | Institutions are an important means for fostering prosocial behaviors, but in many contexts their scope is limited and they govern only a subset of all socially desirable acts. We use a laboratory experiment to study how the presence and nature of an institution that enforces prosocial behavior in one domain affects behavior in another domain and whether it also alters prosocial preferences and beliefs about others’ behavior. Groups play two identical public good games. We vary whether, for only one game, there is an institution enforcing cooperation and vary also whether the institution is imposed exogenously or arises endogenously through voting. Our results show that the presence of an institution in one game generally enhances cooperation in the other game thus documenting a positive spillover effect. These spillover effects are economically substantial amounting up to 30 to 40 percent of the direct effect of institutions. When the institution is determined endogenously spillover effects get stronger over time, whereas they do not show a trend when it is imposed exogenously. Additional treatments indicate that the main driver of this result is not the endogeneity but the temporal trend of the implemented institution. We also find that institutions of either type enhance prosocial preferences and beliefs about others’ prosocial behavior, even toward strangers, suggesting that both factors are drivers of the observed spillover effects. |
| Keywords: | public goods, institutions, spillover effect, social preferences, beliefs |
| JEL: | C92 D02 D72 H41 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_6504&r=gth |
| By: | Camille Cornand (Univ Lyon, CNRS, GATE L-SE UMR 5824, F-69130 Ecully, France); Rodolphe Dos Santos Ferreira (BETA-Strasbourg University, 61 avenue de la Forêt Noire - 67085 Strasbourg Cedex, France; and Catolica Lisbon School of Business and Economics.) |
| Abstract: | We propose a unified framework bridging the gap between team and competition issues, in order to reconsider the social value of private and public information in price and quantity games under imperfect and dispersed information, and to compare the corresponding outcomes in terms of equilibrium and social welfare. The informational distortion associated with the competition motive may lead to a negative social value of private information and reverse the perfect information result in favor of strategic substitutability as the source of higher profit and social welfare. |
| Keywords: | beauty contest, competition, coordination, strategic complementarity, anti-coordination, strategic substitutability, price game, quantity game, dispersed information, public information. |
| JEL: | D43 D82 L13 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:gat:wpaper:1727&r=gth |
| By: | Anton Bondarev; Beat Hintermann; Frank C. Krysiak; Ralph Winkler |
| Abstract: | We study adaptation to climate change in a federalist setting. To protect themselves against an increase in flood risk, regional governments choose among adaptation measures that vary with respect to their costs, the level of protection they offer, and the presence and nature of spillovers to neighboring regions. The central government can provide co-funding in response to specific proposals. If it has to deduce the vulnerability of regions by their actions, the resulting adaptation measures are too costly from a social point of view. The results show that adaptation cannot be expected to be efficient without specifically designed incentive schemes. |
| Keywords: | climate change, adaptation, federalism, asymmetric information, vertical interaction, spillovers, non-cooperative games, signaling |
| JEL: | C72 C73 H23 H41 H77 Q52 Q54 Q58 R53 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_6382&r=gth |
| By: | Dai Zusai (Department of Economics, Temple University) |
| Abstract: | We consider general evolutionary dynamics under idiosyncratic but persistent payoff heterogeneity and study the dynamic relation between the strategy composition over different payoff types and the aggregate strategy distribution of the entire population. It is rigorously proven that continuity of the switching rate function or the type distribution guarantees the existence of a unique trajectory. In major evolutionary dynamics except the standard best response dynamic, an agent's switching rate from the current action to a new action increases with the payoff gain from this switch. This payoff sensitivity makes a heterogeneous dynamic nonaggregable: the transition of the aggregate strategy generically depends not only on the current aggregate strategy but also on the current strategy composition. However, if we look at the strategy composition, stationarity of equilibrium in general and stability in potential games hold under any admissible dynamics. In particular, local stability of each individual equilibrium composition under an admissible dynamic is equivalent to that of the corresponding aggregate equilibrium in the aggregate dynamic induced from the standard best response dynamic, though the basin of attraction may differ over different dynamics. |
| Keywords: | evolutionary dynamics, payoff heterogeneity, aggregation, continuous space, potential games |
| JEL: | C73 C62 C61 |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:tem:wpaper:1702&r=gth |
| By: | Pierre C. Boyer; Kai A. Konrad; Brian Roberson |
| Abstract: | We consider campaign competition in which candidates compete for votes among a continuum of voters by engaging in persuasive efforts that are targetable. Each individual voter is persuaded by campaign effort and votes for the candidate who targets more persuasive effort to this voter. Each candidate chooses a level of total campaign effort and allocates their effort among the set of voters. We completely characterize equilibrium for the majoritarian objective game and compare that to the vote-share maximizing game. If the candidates are symmetric ex ante, both types of electoral competition dissipate the rents from office in expectation. However, the equilibria arising under the two electoral objectives qualitatively differ. In majoritarian elections, candidates randomize over their level of total campaign effort, which provides support for the puzzling phenomenon of the emergence of supermajorities in majoritarian systems. Vote-share maximization leads to an equilibrium in which both candidates make deterministic budget choices and reach a precise fifty-fifty split of vote shares. We also study how asymmetry between the candidates affects the equilibrium. If some share of the voters is loyal to one of the candidates, then both candidates expend the same expected efforts in equilibrium, but the advantaged candidate wins with higher probability for majoritarian voting or a higher share of voters for vote-share maximization. |
| Keywords: | campaign competition, continuous general lotto game, vote buying, flexible budgets, supermajorities, loyal voters |
| JEL: | D72 D78 D82 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_6409&r=gth |
| By: | Laurent Bouton; Benjamin G. Ogden |
| Abstract: | We study the behavior of ethical voters in multicandidate elections. We consider two of the most-widely used electoral rules around the world: the plurality rule and the majority runoff rule. Our model delivers crisper predictions than those of the pivotal voter model. There are two types of equilibria: (i) the sincere voting equilibrium (in which voters vote for their most-preferred candidate), and (ii) Duverger's Law equilibria (in which two candidates attract all the votes). We prove that an equilibrium always exists, and that it is unique for a broad range of parameter values. Moreover, the sincere voting equilibrium never coexists with a Duverger's law equilibrium. We also identify the features of an election that favor sincere voting. Comparing plurality and majority runoff, we find that the incentives to vote sincerely are stronger under the latter. Our results are consistent with the findings of the empirical literature studying strategic voting under plurality and runoff rules. |
| JEL: | C72 D72 |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:23898&r=gth |
| By: | Halkos, George; Papageorgiou, George |
| Abstract: | Public debt accumulation and pollution result to disutility while time path must be sustainable. Policy weapons available to the government with regard to public debt is the generation of primary surpluses to sustain public debt while concerning pollution environmental taxation is expected to reduce emissions. In this paper, we address these factors in a simple dynamic game in order to find ways at which the notions of public debt, pollution, and taxation are interrelated. The starting point of the model is the identity of current account as the equation of motion of public debt, while public debt is considering as a stock and the stress of the regulator is to raise the nation’s primary surplus. Nash and Stackelberg differential game solutions are used to explore the strategic interactions. In the Nash equilibrium establishment of cyclical strategies, during the game between the polluters in one hand and the government on the other, requires that the discount rate of the polluters must be greater than government’s discount rate. That is the polluters must be more impatient than the government. In the case of hierarchical setting, the analytical expressions of the strategic variables and the steady state value of public debt stock are provided. Furthermore, we found the analytical expressions of the value functions, making, therefore, the policy implications an easy task. Finally, we found the conditions under which the conflict is more intensive, in the two cases of equilibrium, according to the shadow price of the environmental damages. |
| Keywords: | Public debt; Pollution; Taxation; Dynamic games; Nash equilibrium; Stackelberg equilibrium. |
| JEL: | C72 H23 H62 Q52 Q53 Q58 |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:81982&r=gth |
| By: | Yao Cheng; Zaifu Yang |
| Abstract: | This paper considers a general and practical kidney exchange model with compatible or incompatible patient-donor pairs, single donors, and patients on the waiting list. Efficient exchange procedures are proposed with dichotomous preferences in which only one-way, two-way, three, or four-way chains or cycles of exchange are used. We derive a tight upper bound of the possible number of feasible kidney transplants in each case of exchange and provide substantial simulation results. We find that two-way cycles and chains of exchange can substantially increase the number of feasible transplants, threeway can have a visible effect, and at most four-way cycles and chains suffice to capture all potential gains of exchange. Our results are not only theoretically interesting but also have meaningful policy implications. |
| Keywords: | Kidney Exchange, Efficiency, Matching, Simulation. |
| JEL: | C78 |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:yor:yorken:17/13&r=gth |
| By: | Yinbo Feng (School of Management, Fudan University, Shanghai, China, 200433); Ming Hu (Rotman School of Management, University of Toronto, Toronto, Ontario, Canada M5S 3E6) |
| Abstract: | We provide a theory unifying the long tail and blockbuster phenomenon. Specifically, we analyze a three-stage game where the firms first make entry decisions, then decide on the investment in its product and lastly customers sequentially arrive to make purchase decisions based on product quality and historic sales under the network effect. We analytically show that a growing network effect always contributes to the demand concentration on a small number of products. However, product variety and quality investments, as an outcome of firms¡¯ ex-ante competitive decisions, may increase or decrease, as the network effect grows. When the network effect parameter is smaller than a threshold, the increasing network effect would shift more demand towards the products with higher qualities, preempting more products from entering the market ex ante and inducing firms to adopt the blockbuster equilibrium strategy by making larger quality investment. When the network effect is stronger than the threshold, the increasing network effect would make the market easily concentrated to a few products. Even some low quality ones may have chances to become a ¡°hit.¡± Interestingly, in this case, the ex-ante equilibrium product variety would be broader and firms adopt the niche equilibrium strategy by maker smaller quality investment. We empirically test the theory with the movie box office data and find strong supporting evidence. |
| Keywords: | long tail; blockbuster; niche; product variety; network effect |
| JEL: | C72 D43 L11 L25 M21 |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:net:wpaper:1713&r=gth |
| By: | Topi Miettinen; Michael Kosfeld; Ernst Fehr; Jörgen W. Weibull |
| Abstract: | We experimentally investigate behavior and beliefs in a sequential prisoner’s dilemma. Each subject had to choose an action as first-mover and a conditional action as second-mover. All subjects also had to state their beliefs about others’ second-mover choices. We find that subjects’ beliefs about others’ choices are fairly accurate on average. Using the elicited beliefs, we compare the explanatory power of a few current models of social and moral preferences. The data show clear differences in explanatory power between the preference models, both without and with control for the number of free parameters. The best-performing models explain about 80% of observed behavior. We use the estimated preference parameters to identify biases in subjects’ expectations. We find a consensus bias (whereby subjects believe others behave like themselves) and a certain optimism (whereby subjects overestimate probabilities for favorable outcomes), the former being about twice as strong as the second. |
| Keywords: | cooperation, prisoners’ dilemma, other-regarding preferences, categorical imperative, consensus effect, optimism |
| JEL: | C72 C90 D03 D84 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_6358&r=gth |
| By: | Gu, Yiquan; Hehenkamp, Burkhard; Leininger, Wolfgang |
| Abstract: | We study evolutionarily stable strategy (ESS) in contests where participation is stochastic. When participation probabilities are given, players exert more effort In ESS than under Nash. Ex-ante overdissipation occurs when participation is suff. likely and discriminative power of the contest suff. high. When entry is costly and endogenous, players’ entry is more likely, more costly, and less profitable in ESS than under Nash. Ex-ante overdissipation also occurs for concave impact functions. |
| JEL: | D72 C73 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc17:168168&r=gth |
| By: | Remy Oddou |
| Abstract: | This paper analyses the effect of allowances, whose amount depends on jurisdictions, on the segregative properties of endogenous formation of jurisdictions. Households choosing to live at the same place form a jurisdiction whose aim is to produce a local public good and to implement a redistribution policy, by granting every household an allowance whose amount is determined by the jurisdiction. In every jurisdiction, the production of the local public services and the allowance are financed with a local tax based upon the households’ wealth. Local wealth tax rates and the level of the allowance are exogenously determined in every jurisdiction. Households are free to leave their jurisdiction for another jurisdiction that would provide them with their highest utility. We find that the existence of an allowance mitigates the segregative properties of endogenous jurisdiction formation, as the condition identified by Gravel and Thoron to ensure the segregation of any stable jurisdiction structure remains necessary, but is no longer sufficient. |
| Keywords: | Jurisdictions; Segregation; Allowance |
| JEL: | C78 D02 H73 R13 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:drm:wpaper:2017-42&r=gth |
| By: | Remy Oddou |
| Abstract: | This paper analyses how welfarism affects the segregative properties of endogenous jurisdiction formation, in a model where local jurisdictions produce a local public good and distribute an allowance to their households, both financed by a proportional tax based on the households' wealth. A jurisdiction is composed of all the households that live in the same place. Local wealth tax rates and the level of the allowance are determined to maximize a social welfare function. Households can "vote with their feet", which means that they can choose to move to the jurisdiction that offers the package "tax rate - amount of public good - allowance" that provides the highest utility level. The main result of this article is the proof that the maximin criterium is more segregative than the utilitarian one. |
| Keywords: | Jurisdiction, Segregation, Welfare |
| JEL: | C78 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:drm:wpaper:2017-43&r=gth |