|
on Game Theory |
| By: | Bavly, Gilad; Heller, Yuval; Schreiber, Amnon |
| Abstract: | We consider games in which players search for a hidden prize, and they have asymmetric information about the prize's location. We study the social payoff in equilibria of these games. We present sufficient conditions for the existence of an equilibrium that yields the first-best payoff (i.e., the highest social payoff under any strategy profile), and we characterize the first-best payoff. The results have interesting implications for innovation contests and R&D races. |
| Keywords: | search duplication, decentralized research, social welfare, incomplete information |
| JEL: | C72 D82 D83 |
| Date: | 2020–02–27 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:98838&r=all |
| By: | Fabrice Barthelemy; Mathieu Martin (Université de Cergy-Pontoise, THEMA) |
| Abstract: | This paper is a companion paper of Barthelemy et al. (2019) which studies the role of the quota on the occurrence of "dummy" players in small weighted voting games (i.e., in voting games with 3, 4 or 5 players). We here extend the results obtained in this paper by considering voting games with a larger number of players (up to 15). It is shown that the probability of having a player without voting power is very sensitive to the choice of the quota and the quota values that minimize this probability are derived. |
| Keywords: | Cooperative game theory, weighted voting games, dummy player, probability of voting paradoxes. |
| JEL: | C7 D7 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:ema:worpap:2020-01&r=all |
| By: | P. Jean-Jacques Herings (Department of Economics, Maastricht University); Riccardo D. Saulle (DSEA, University of Padova); Christian Seel (Department of Economics, Maastricht University) |
| Abstract: | This paper studies coalition formation among individuals who differ in productivity. The output of a coalition is determined by the sum of the productivities and the size of the coalition. We consider egalitarian societies in which coalitions split their surplus equally and individualistic societies in which the surplus of a coalition is split according to productivity. Preferences of coalition members depend on their material payoffs, but are also influenced by relative payoff concerns, which relate their material payoffs to the average material payoff in the coalition. Our analysis uses two stability notions, the Core and the Myopic Stable Set. The stable partitions in both egalitarian and individualistic societies are segregated, i.e., individuals with adjacent productivities form coalitions. If some individuals are not part of a productive coalition, then these are the least productive ones for egalitarian societies and the most productive ones for individualistic societies. If all individuals have different productivity levels and there are sufficient complementarities in production, egalitarian societies induce more efficiency than individualistic societies. |
| Keywords: | Group Formation, Segregation, Relative Payoff, Egalitarianism, Meritocracy, Social Environment |
| JEL: | C70 C71 D62 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:pad:wpaper:0249&r=all |
| By: | Emin Karagözoglu; Cagri Saglam; Agah R. Turan |
| Abstract: | We model the dynamic contest between two players as a game of tug-of-war with a Tullock contest success function (CSF). We show that (pure strategy) Markov perfect equilibrium of this game exists, and it is unique. In this equilibrium - in stark contrast to a model of tug-of-war with an all pay auction CSF - players exert positive efforts until the very last battle. Since the outcome of an individual battle is determined stochastically, even disadvantaged players who fell behind will occasionally win battles and hence the advantage likely change hands. We deliver a set of empirically appealing results on effort dynamics. |
| Keywords: | contests, discouragement effect, perseverance, stochastic games, tug-of-war, Tullock contest success function |
| JEL: | C72 D72 D74 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_8103&r=all |
| By: | Emin Karagözoglu; Kerim Keskin; Cagri Saglam |
| Abstract: | We introduce a model of product development in a firm. Our model describes the process as a multi-stage contest (i.e., race) with an endogenous length (with one stage or two stages) between two workers. We model the payments to workers from the new product using the normatively appealing Nash bargaining solution (see Nash, 1950). In our model the disagreement payoffs endogenously depend on the contest outcome. More precisely, a bargaining advantage is given to the leading worker in the product development contest. We analytically characterize subgame perfect equilibrium effort levels of workers and describe the conditions under which a full-edged final (as opposed to, say, a prototype) product is developed. Our comparative static analyses reveal economically intuitive insights. Finally, we provide an answer to the firm’s problem of optimal incentive provision (considering both collective and individual incentives). |
| Keywords: | product development, contests, Nash bargaining solution, optimal contracts, subgame perfect Nash equilibrium, race |
| JEL: | C72 C78 D86 O31 O32 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_8109&r=all |
| By: | Schouten, Jop (Tilburg University, Center For Economic Research); Saavedra-Nieves, Alejandro; Fiestras-Janeiro, G. |
| Abstract: | This paper studies sequencing situations with non-linear cost functions. We show that the neighbor switching gains are now time-dependent, in contrast to the standard sequencing situations with linear cost functions, which complicate finding an optimal order and stable allocations. We derive conditions on the time-dependent neighbor switching gains in a (general) sequencing situation to guarantee convexity of the associated sequencing game. Moreover, we provide two procedures that uniquely specify a path from the initial order to an optimal order and we define two corresponding allocation rules that divide the neighbor switching gains equally in every step of the path. We show that the same conditions on the gains also guarantee stability for the allocations prescribed by these rules. |
| Keywords: | sequencing games; non-linear cost functions; Time-dependent neighbor switching gains; covexity; stable allocations |
| JEL: | C44 C71 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiucen:3e1db5c9-0f77-4f91-a075-c01a9ea30b70&r=all |
| By: | Dietzenbacher, Bas (Tilburg University, Center For Economic Research); Yanovskaya, E. |
| Abstract: | This note shows that the egalitarian Dutta and Ray (1989) solution for transferable utility games is self-antidual on the class of exact partition games. By applying a careful antiduality analysis, we derive several new axiomatic characterizations. Moreover, we point out an error in earlier work on antiduality and repair and strengthen several related characterizations on the class of convex games. |
| Keywords: | transferable utility games; egalitarianism; antiduality; exact partition games; Convex games |
| JEL: | C71 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiucen:0b8133f8-cab7-46ae-8881-03cb32f26843&r=all |
| By: | Proto, Eugenio (University of Glasgow); Rustichini, Aldo (University of Minnesota); Sofianos, Andis (Heidelberg University) |
| Abstract: | A large literature in behavioral economics has emphasized in the last decades the role of individual differences in social preferences (such as trust and altruism) and in influencing behavior in strategic environments. Here we emphasize the role of attention and working memory, and show that social interactions among heterogeneous groups are likely to be mediated by differences in cognitive skills. Our design uses a Repeated Prisoner's Dilemma, and we compare rates of cooperation in groups of subjects grouped according to their IQ, with those in combined groups. While in combined groups we observe higher cooperation rates and profits than in separated groups (with consistent gains among lower IQ subjects and relatively smaller losses for higher IQ subjects), higher IQ subjects become less lenient when they are matched with lower IQ subjects than when they play separately. We argue that this is an instance of a general phenomenon, which we demonstrate in an evolutionary game theory model, where higher IQ among subjects determines – through better working memory – a lower frequency of errors in strategy implementation. In our data, we show that players indeed choose less lenient strategies in environments where subjects have higher error rates. The estimations of errors and strategies from the experimental data are consistent with the hypothesis and the predictions of the model. |
| Keywords: | IQ, intelligence, cooperation, repeated Prisoner's Dilemma, strategy, error in transition |
| JEL: | C73 C91 C92 |
| Date: | 2020–01 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp12925&r=all |
| By: | William C. Horrace (Center for Policy Research, Maxwell School, Syracuse University, 426 Eggers Hall, Syracuse, NY 13244); Hyunseok Jung (Department of Economics, University of Arkansas); Shane Sanders (Department of Sports Management, Syracuse University) |
| Abstract: | We consider a heterogeneous social interaction model where agents interact with peers within their own network but also interact with agents across other (non-peer) networks. To address potential endogeneity in the networks, we assume that each network has a central planner who makes strategic network decisions based on observable and unobservable characteristics of the peers in her charge. The model forms a simultaneous equation system that can be estimated by Quasi-Maximum Likelihood. We apply a restricted version of our model to data on National Basketball Association games, where agents are players, networks are individual teams organized by coaches, and competition is head-to-head. That is, at any time a player only interacts with two networks: their team and the opposing team. We find significant positive within-team peer-effects and both negative and positive opposing-team competitor-effects in NBA games. The former are interpretable as “team chemistries" which enhance the individual performances of players on the same team. The latter are interpretable as “team rivalries," which can either enhance or diminish the individual performance of opposing players. |
| Keywords: | Spatial Analysis, Peer Effects, Endogeneity, Machine Learning |
| JEL: | C13 C31 D24 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:max:cprwps:226&r=all |
| By: | Benjamin M. Hébert; Jennifer La'O |
| Abstract: | This paper analyzes non-fundamental volatility and efficiency in a class of large games (including e.g. linear-quadratic beauty contests) that feature strategic interaction and endogenous information acquisition. We adopt the rational inattention approach to information acquisition but generalize to a large class of information costs. Agents may learn not only about exogenous states, but also about endogenous outcomes. We study how the properties of the agents’ information cost relate to the properties of equilibria in these games. We provide the necessary and sufficient conditions information costs must satisfy to guarantee zero non-fundamental volatility in equilibrium, and provide another set of necessary and sufficient conditions to guarantee equilibria are efficient. We show in particular that mutual information, the cost function typically used in the rational inattention literature, both precludes non-fundamental volatility and imposes efficiency, whereas the Fisher information cost introduced by Hébert and Woodford [2020] generates both non-fundamental volatility and inefficiency. |
| JEL: | C72 D62 D83 |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:26771&r=all |
| By: | Juan D. Moreno-Ternero (Department of Economics, Universidad Pablo de Olavide;); Min-Hung Tsay (Department of Economics, National Chung Cheng University); Chun-Hsien Yeh (Institute of Economics, Academia Sinica; Chung-Hua Institute for Economic Research) |
| Abstract: | We follow the Nash program to provide a new strategic justification for the Talmud rule to solve bankruptcy problems. The design of our game is based on a focal characterization of the rule, obtained when combining consistency with two properties guaranteeing meaningful lower and upper bounds to all creditors. |
| Keywords: | Nash program; strategic justification; consistency; lower bounds; upper bounds; Talmud rule |
| JEL: | C71 C72 D63 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:pab:wpaper:20.02&r=all |
| By: | David Rojo-Arjona (The George L Argyros School of Business and Economics, Chapman University.); R. Stefania Sitzia (School of Economics and Centre for Behavioural and Experimental Social Science, University of East Angle, Norwich.); Jiwei Zheng (School of Economics and Centre for Behavioural and Experimental Social Science, University of East Anglia, Norwich) |
| Abstract: | We report an experiment that investigates whether increasing the saliency of the focal point, increases coordination success in tacit coordination and bargaining games. We find unexpectedly high coordination rates not only when the degree of conflict is small but also when it is large. This provides supports to the conjecture that conflict of interests reduces the saliency of the focal point relative to saliency of the payoffs, and because of this, even small payoffs differences lead to significant mis-coordination. Increasing the saliency of the focal point has the effect of drawing attention away from the conflicting payoffs and towards the focal point, restoring its effectiveness as coordination devices. Increased saliency has also the effect of shifting choices from less to more unequal, and sometimes more efficient, outcomes. This results in greater coordination success on the outcome suggested by the payoff-irrelevant cue. Overall coordination success however does not increase. |
| Keywords: | Focal points; Coordination; Conflict of interest; Payoff-irrelevant cues. |
| JEL: | C78 C91 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:uea:wcbess:20-02&r=all |
| By: | Mariola Ndrio; Khaled Alshehri; Subhonmesh Bose |
| Abstract: | We consider a market in which both suppliers and consumers compete for a product via scalar-parameterized supply offers and demand bids. Scalar-parameterized offers/bids are appealing due to their modeling simplicity and desirable mathematical properties with the most prominent being bounded efficiency loss and price markup under strategic interactions. Our model incorporates production capacity constraints and minimum inelastic demand requirements. Under perfect competition, the market mechanism yields allocations that maximize social welfare. When market participants are price-anticipating, we show that there exists a unique Nash equilibrium, and provide an efficient way to compute the resulting market allocation. Moreover, we explicitly characterize the bounds on the welfare loss and prices observed at the Nash equilibrium. |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2003.01206&r=all |
| By: | Chantreuil, Frédéric (University of New Caledonia); Fourrey, Kévin; Lebon, Isabelle (University of Caen); Rebiere, Therese (CNAM, Paris) |
| Abstract: | This paper is an application of a new Shapley income decomposition methodology, in which we isolate two subjective factors in income differences - race and gender - that contribute to income inequality within the population of blacks and whites in the United States over the period 2005-2017. We show that the purely racial contribution to income inequality as defined by the Gini index varies from 1% to 4% depending on the geographical administrative divisions used. Race tends to contribute more to inequality in the Western and Southern part of the country. Whatever the division, the share of income inequality associated with gender exceeds greatly that of race. While gender income inequality falls over time, income inequality associated with race tends to increase. |
| Keywords: | income inequality, decomposition, Shapley value, racial discrimination, gender discrimination |
| JEL: | C71 D63 J15 J71 |
| Date: | 2020–01 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp12950&r=all |
| By: | Thomas Spooner; Rahul Savani |
| Abstract: | We show that adversarial reinforcement learning (ARL) can be used to produce market marking agents that are robust to adversarial and adaptively chosen market conditions. To apply ARL, we turn the well-studied single-agent model of Avellaneda and Stoikov [2008] into a discrete-time zero-sum game between a market maker and adversary, a proxy for other market participants who would like to profit at the market maker's expense. We empirically compare two conventional single-agent RL agents with ARL, and show that our ARL approach leads to: 1) the emergence of naturally risk-averse behaviour without constraints or domain-specific penalties; 2) significant improvements in performance across a set of standard metrics, evaluated with or without an adversary in the test environment, and; 3) improved robustness to model uncertainty. We empirically demonstrate that our ARL method consistently converges, and we prove for several special cases that the profiles that we converge to are Nash equilibria in a corresponding simplified single-stage game. |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2003.01820&r=all |
| By: | Itai Arieli; Yakov Babichenko; Fedor Sandomirskiy; Omer Tamuz |
| Abstract: | We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state and who observe some information structure. Our main result is that, for the two agent case, a quantitative version of Aumann's Agreement Theorem provides a necessary and sufficient condition for feasibility. We use our characterization to construct joint belief distributions in which agents are informed regarding the state, and yet receive no information regarding the other's posterior. We also study a related class of Bayesian persuasion problems with a single sender and multiple receivers, and explore the extreme points of the set of feasible distributions. |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2002.11362&r=all |
| By: | Sobhani, S. Omid (Sharif University of Technology); Sheykhha, Siamak (E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN)); Madlener, Reinhard (E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN)) |
| Abstract: | The integration of energy hubs – as an important component of future energy networks that will employ demand-side management techniques – has a key role in the process of efficiency improvement and reliability enhancement of power grids. In such power grids, energy hub operators need to optimally schedule the consumption, conversion, and storage of available resources based on their own utility functions. In sufficiently large networks, scheduling an individual hub can affect the utility of the other energy hubs. In this paper, the interaction between energy hubs is modeled as a potential game. Each energy hub operator (player) participates in a dynamic energy pricing market and tries to maximize his own payoff with regard to energy consumption satisfaction. We propose a distributed algorithm based on a potential game, which guarantees the existence of a Nash equilibrium. Furthermore, two different types of signaling are developed and simulation results are compared. Simulation results show that with the implementation of either setup the peak-to-average ratio between electricity networks and natural gas networks diminishes. An analysis of the results shows that either setup can have superiority over the other one with regard to generation costs, convergence rate, price level, and the stability perspective. Hence, energy providers and consumers can choose a favorable setup based on their respective needs. |
| Keywords: | Smart Energy Hub (SEH); Integrated Demand-Response Program; Distributed Demand-Side Management; Storage System |
| JEL: | C61 C72 Q31 Q41 |
| Date: | 2018–11 |
| URL: | http://d.repec.org/n?u=RePEc:ris:fcnwpa:2018_014&r=all |
| By: | Indrajit Saha; Veeraruna Kavitha |
| Abstract: | We consider a random financial network with a large number of agents. The agents connect through credit instruments borrowed from each other or through direct lending, and these create the liabilities. The settlement of the debts of various agents at the end of the contract period can be expressed as solutions of random fixed point equations. Our first step is to derive these solutions (asymptotically), using a recent result on random fixed point equations. We consider a large population in which agents adapt one of the two available strategies, risky or risk-free investments, with an aim to maximize their expected returns (or surplus). We aim to study the emerging strategies when different types of replicator dynamics capture inter-agent interactions. We theoretically reduced the analysis of the complex system to that of an appropriate ordinary differential equation (ODE). We proved that the equilibrium strategies converge almost surely to that of an attractor of the ODE. We also derived the conditions under which a mixed evolutionary stable strategy (ESS) emerges; in these scenarios the replicator dynamics converges to an equilibrium at which the expected returns of both the populations are equal. Further the average dynamics (choices based on large observation sample) always averts systemic risk events (events with large fraction of defaults). We verified through Monte Carlo simulations that the equilibrium suggested by the ODE method indeed represents the limit of the dynamics. |
| Date: | 2020–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2003.00886&r=all |
| By: | Cristina Bicchieri; Eugen Dimant; Silvia Sonderegger |
| Abstract: | We experimentally investigate whether individuals strategically distort their beliefs about dominant norms. Embedded in the context of lying, we systematically vary both the nature of elicited beliefs (descriptive about what others do, or normative about what others approve of) and whether subjects are aware of the forthcoming lying opportunity at the belief-formation stage. We build a dual-self model of belief distortion applied to the context of social norms and derive a number of precise predictions. Our findings provide a perspective on why, when and which norm-relevant beliefs are strategically distorted and show that not all belief distortions are created equal. |
| Keywords: | lying, social norms, strategic beliefs, uncertainty |
| JEL: | C72 C91 D80 D90 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_8059&r=all |
| By: | Noha Elboghdadly (University of Bath, UK); Michael Finus (University of Graz, Austria) |
| Abstract: | Carbon leakage and the relocation of rms is one of the main concerns of governments when choosing their climate policy. In a strategic trade model with endogenous plant location, we study the effect of border carbon adjustments (BCAs) on equilibrium emission taxes in a non-cooperative policy game between two asymmetric countries. To this end, we compare a No-BCA regime with a BCA regime for two scenarios: a simultaneous and a sequential game. Without BCAs, a “race to the bottom” is the only Nash equilibrium. In a Stackelberg equilibrium, a second less negative outcome may emerge, which constitutes a Pareto-improvement to all governments. In this “wise chicken equilibrium”, the Stackelberg leader gives in, letting his/her firms relocate in order to avoid the race-to-the-bottom equilibrium. With BCAs, the race-to-the-bottom in carbon taxes can be avoided in the Nash equilibrium and also in Stackelberg equilibria global emissions are reduced. We show that the country imposing BCAs is always better off, global welfare usually increases with BCAs, even though the country on which BCAs are imposed may be better worse off. We characterize those conditions. |
| Keywords: | Endogenous plant location; global emissions; emission tax competition; border carbon adjustments |
| JEL: | F12 F18 H23 H87 Q58 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:grz:wpaper:2020-07&r=all |