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on Game Theory |
| By: | Moshe Babaioff; Uriel Feige |
| Abstract: | We consider transferable-utility profit-sharing games that arise from settings in which agents need to jointly choose one of several alternatives, and may use transfers to redistribute the welfare generated by the chosen alternative. One such setting is the Shared-Rental problem, in which students jointly rent an apartment and need to decide which bedroom to allocate to each student, depending on the student's preferences. Many solution concepts have been proposed for such settings, ranging from mechanisms without transfers, such as Random Priority and the Eating mechanism, to mechanisms with transfers, such as envy free solutions, the Shapley value, and the Kalai-Smorodinsky bargaining solution. We seek a solution concept that satisfies three natural properties, concerning efficiency, fairness and decomposition. We observe that every solution concept known (to us) fails to satisfy at least one of the three properties. We present a new solution concept, designed so as to satisfy the three properties. A certain submodularity condition (which holds in interesting special cases such as the Shared-Rental setting) implies both existence and uniqueness of our solution concept. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.11346&r=all |
| By: | Sam Ganzfried; Conner Laughlin; Charles Morefield |
| Abstract: | Many real-world domains contain multiple agents behaving strategically with probabilistic transitions and uncertain (potentially infinite) duration. Such settings can be modeled as stochastic games. While algorithms have been developed for solving (i.e., computing a game-theoretic solution concept such as Nash equilibrium) two-player zero-sum stochastic games, research on algorithms for non-zero-sum and multiplayer stochastic games is very limited. We present a new algorithm for these settings, which constitutes the first parallel algorithm for multiplayer stochastic games. We present experimental results on a 4-player stochastic game motivated by a naval strategic planning scenario, showing that our algorithm is able to quickly compute strategies constituting Nash equilibrium up to a very small degree of approximation. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.00193&r=all |
| By: | Lian Xue (Wuhan University); Stefania Sitzia (University of East Anglia); Theodore L. Turocy (University of East Anglia) |
| Abstract: | We use experimental methods to test the effects of joint endowment on coordination success in tacit bargaining games. It has been well established that people use existing focal points to facilitate coordination and the power of such cues declines as payoff becomes increasingly unequal. We conducted an experiment in which two players jointly engaged in an interactive team building activity and together earned the stakes over which they bargain. In the team building exercise, two players jointly complete a shortest route task in a metaphor of a treasure hunt. After the two treasure hunters complete the journey, they independently decide how to divide their rewards using a tacit bargaining table. We find that when participants bargain over the fruits that result from joint activity, they are more likely to coordinate the focal point equilibrium. |
| Keywords: | Team building; Joint production; Group identity; Tacit bargaining; Focal point |
| JEL: | C72 C91 C92 |
| Date: | 2017–11–27 |
| URL: | http://d.repec.org/n?u=RePEc:uea:wcbess:17-12&r=all |
| By: | Yukihiko Funaki (Waseda University); Harold Houba (Vrije Universiteit Amsterdam); Evgenia Motchenkova (Vrije Universiteit Amsterdam) |
| Abstract: | We develop a novel model of price-fee competition in bilateral oligopoly markets with non-expandable infrastructures and costly transportation. The model captures a variety of real market situations and it is the continuous quantity version of the assignment game with indivisible goods on a fixed network. We define and characterize stable market outcomes. Buyers exclusively trade with the supplier with whom they achieve maximal bilateral joint welfare at prices equal to marginal costs. Maximal fees and the suppliers' market power are restricted by the buyers' credible threats to switch suppliers. Maximal fees also arise from a negotiation model that extends price competition to price-fee competition. Competition in both prices and fees necessarily emerges. It improves welfare compared to price competition, but buyers will not be better off. The minimal infrastructure achieving maximal aggregate welfare differs from the minimal network that protects buyers most. |
| Keywords: | Assignment Games, Infrastructure, Non-linear pricing, Market Power, Negotiations |
| JEL: | D43 C78 L1 |
| Date: | 2019–09–27 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20190070&r=all |
| By: | Ensthaler, Ludwig; Huck, Steffen; Leutgeb, Johannes |
| Abstract: | From the regulation of sports to lawmaking in parliament, in many situations one group of people ("agents") make decisions that affect the payoffs of others ("principals") who may offer action-contingent transfers in order to sway the agents' decisions. Prat and Rustichini (2003) characterize pure-strategy equilibria of such Games Played Through Agents. Specifically, they predict the equilibrium outcome in pure strategies to be efficient. We test the theory in a series of experimental treatments with human principals and computerized agents. The theory predicts remarkably well which actions and outcomes are implemented but subjects' transfer offers deviate systematically from equilibrium. We show how quantal response equilibrium accounts for the deviations and test its predictions out of sample. Our results show that quantal response equilibrium is particularly well suited for explaining behavior in such games. |
| Keywords: | games played through agents,experiment,quantal response equilibrium |
| JEL: | D44 C91 D72 D83 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:wzbeoc:spii2016305r2&r=all |
| By: | Godfrey Keller; Sven Rady |
| Abstract: | We analyze undiscounted continuous-time games of strategic experimentation with two-armed bandits. The risky arm generates payoffs according to a L\'{e}vy process with an unknown average payoff per unit of time which nature draws from an arbitrary finite set. Observing all actions and realized payoffs, players use Markov strategies with the common posterior belief about the unknown parameter as the state variable. We show that the unique symmetric Markov perfect equilibrium can be computed in a simple closed form involving only the payoff of the safe arm, the expected current payoff of the risky arm, and the expected full-information payoff, given the current belief. In particular, the equilibrium does not depend on the precise specification of the payoff-generating processes. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.13323&r=all |
| By: | Lorenzo, Cerboni Baiardi; Ahmad, Naimzada |
| Abstract: | We consider the competition among quantity setting players in a linear evolutionary environment. To set their outputs, players adopt, alternatively, the best response rule having perfect foresight or an imitative rule. Players are allowed to change their behavior through an evolutionary mechanism according to which the rule with better performance will attract more followers. The relevant stationary state of the model describes a scenario where players produce at the Cournot-Nash level. Due to the presence of imitative behavior, we find that the number of players and implementation costs, needed to the best response exploitation, have an ambiguous role in determining the stability properties of the equilibrium and double stability thresholds can be observed. Differently, the role of the intensity of choice, representing the evolutionary propensity to switch to the most profitable rule, has a destabilizing role, in line with the common occurrence in evolutionary models. The global analysis of the model reveals that increasing values of the intensity of choice parameter determine increasing dynamic complexities for the internal attractor representing a population where both decision mechanisms coexist. |
| Keywords: | Imitation, heterogeneity, evolutionary game, replicator dynamics, dynamic instability, dynamical systems |
| Date: | 2019–05 |
| URL: | http://d.repec.org/n?u=RePEc:mib:wpaper:407&r=all |
| By: | Margarita Gáfaro (Banco de la República de Colombia); César Mantilla |
| Abstract: | Divisions of rural land in developing countries reduce the possibilities of farmers to profit from agricultural returns to scale. We design and conduct a framed bargaining experiment to study whether land overvaluation (due to affective reasons) and uncertainty in land values are drivers for land division. In our bargaining game, two players with different agricultural productivity jointly inherit a land plot and individually inherit some tokens they can use to agree on a land allocation. The possible set of land allocations and the spread of land returns vary across treatment arms in the game. We conduct this experiment with 256 participants in eight rural municipalities of the Northeast of Colombia. We find that when players are allowed to divide the land plot, 75% of the bargaining interactions yield the most egalitarian, but less efficient, land allocations. Based on the predictions of a Nash bargaining model and the observations from a sample of 120 college students, we rule out land overvaluation as a driver for land divisions in the context of our game. We also find that uncertainty in land yields reduces the efficiency of land allocations when we do not allow land divisions, by increasing the likelihood of the least productive player keeping the entire land plot. Our results are consistent with a bounded rationality rule in which subjects incorporate a behavioral response to uncertainty by first bargaining over land, which is a certain outcome, and then bargaining over a token transfer. **** RESUMEN: Las divisiones de tierras rurales en los países en desarrollo limitan las posibilidades de los agricultores en estos países de aprovechar economías de escala derivadas de la mecanización. Diseñamos y llevamos a cabo un experimento de negociación para explorar si la sobrevaloración de la tierra (debido a razones afectivas) y la incertidumbre sobre el valor de la tierra explican divisiones ineficientes de tierras en contextos agrícolas. En nuestro juego de negociación, dos jugadores con diferentes niveles de productividad agrícola heredan conjuntamente una parcela de tierra e individualmente heredan algunas fichas que pueden usar para acordar una repartición de la parcela. Variamos aleatoriamente, entre grupos de tratamiento en el juego, el conjunto de posibles reparticiones de la parcela y la dispersión de los retornos de la tierra. Llevamos a cabo este experimento con 256 participantes en ocho municipios rurales del nororiente de Colombia. Encontramos que cuando se permite a los jugadores dividir la parcela, el 75% de las interacciones de negociación generan las asignaciones de tierra más igualitarias, pero menos eficientes. Con base en las predicciones de un modelo de negociación de Nash y las observaciones de una muestra de 120 estudiantes universitarios, descartamos la sobrevaluación de la tierra como motor de divisiones de tierra en el contexto de nuestro juego. Por otro lado, encontramos que una mayor incertidumbre en los rendimientos de la tierra reduce la eficiencia en las asignaciones de tierra cuando eliminamos las divisiones igualitarias del conjunto de posibles reparticiones. Nuestros resultados son consistentes con una regla de racionalidad limitada en la cual los sujetos incorporan una respuesta conductual a la incertidumbre, al negociar primero sobre una asignacin de tierra, que es un resultado fijo y determinado, y luego negociar sobre una transferencia de fichas. |
| Keywords: | Land division, Nash bargaining, affective value of land, nonuse value, División de tierras, negociación de Nash, valor afectivo, valor de no uso |
| JEL: | C78 C90 O13 Q15 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:bdr:borrec:1092&r=all |
| By: | Juan Passadore (Einaudi Institute for Economics and Fina); Juan Xandri (Princeton) |
| Abstract: | Dynamic policy games feature a wide range of equilibria. This paper provides a methodology for obtaining robust predictions. We begin by focusing on a model of sovereign debt although our methodology applies to other settings, such as models of monetary policy or capital taxation. The main result of the paper is a characterization of outcomes that are consistent with a subgame perfect equilibrium conditional on the observed history. Our methodology provides observable implications common across all equilibria that we illustrate by characterizing, conditional on an observed history, the set of all possible continuation prices of debt and comparative statistics for this set; by computing bounds on the maximum probability of a crisis; and by obtaining bounds on means and variances. In addition, we propose a general dynamic policy game and show how our main result can be extended to this general environment. |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:red:sed019:1345&r=all |
| By: | Sofia Moroni |
| Abstract: | We consider continuous time games in which players have stochastic opportunitiesto move before a deadline. In this paper we define notions of trembling handand sequential equilibrium and show that both types of equilibria exist in a large classof such games that may feature incomplete and imperfect information. These gamesmodel realistic non-stationary dynamic situations in which players do not know exactlywhen they or their opponents will be able to move. In the complete informationcase we establish existence of a Markov Perfect equilibrium. |
| Date: | 2019–01 |
| URL: | http://d.repec.org/n?u=RePEc:pit:wpaper:6757&r=all |
| By: | Oksana Loginova (Department of Economics, University of Missouri) |
| Abstract: | The focus of this theoretical study is price competition when some firms operate their own branded websites while others sell their products through an online platform, such as Amazon Marketplace. On one hand, selling through Amazon expands a firm's reach to more customers, but on the other, starting a website can help the firm to increase the perceived value of its product, that is, to build brand equity. In the short run the composition of firms is fixed, whereas in the long run each firm chooses between Amazon and its own website. I derive the equilibrium prices and profits, analyze the firms' behavior in the long run, and compare the equilibrium outcome with the social optimum. Comparative statics analysis reveals some interesting results. For example, I find that the number of firms that choose Amazon may go down in response to an increase in the total number of firms. A pure-strategy Nash equilibrium may not exist; I show that price dispersion among the firms of the same type is more likely in less concentrated markets and/or when the increase in the perceived value of the product is relatively small. |
| Keywords: | pricing, competition, platforms, online marketplace, Amazon, brand equity |
| JEL: | C72 D43 L11 L13 M31 |
| Date: | 2019–09–20 |
| URL: | http://d.repec.org/n?u=RePEc:umc:wpaper:1906&r=all |
| By: | S\"oren Christensen; Kristoffer Lindensj\"o |
| Abstract: | For a discrete time Markov chain and in line with Strotz' consistent planning we develop a framework for problems of optimal stopping that are time-inconsistent due to the consideration of a non-linear function of an expected reward. We consider pure and mixed stopping strategies and a (subgame perfect Nash) equilibrium. We provide different necessary and sufficient equilibrium conditions including a verification theorem. Using a fixed point argument we provide equilibrium existence results. We adapt and study the notion of the myopic adjustment process and introduce different kinds of equilibrium stability. We show that neither existence nor uniqueness of equilibria should generally be expected. The developed theory is applied to a mean-variance problem and a variance problem. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.11921&r=all |
| By: | Kayaba Yutaka (Faculty of Economics, The University of Tokyo); Hitoshi Matsushima (Faculty of Economics, The University of Tokyo); Tomohisa Toyama (College of Liberal Arts, International Christian University) |
| Abstract: | e experimentally examine repeated prisoner’s dilemma with random termination, in which monitoring is imperfect and private. Our estimation indicates that a significant proportion of the subjects follow generous tit-for-tat strategies, which are stochastic extensions of tit-for-tat. However, the observed retaliating policies are inconsistent with the generous tit-for-tat equilibrium behavior. Showing inconsistent behavior, subjects with low accuracy do not tend to retaliate more than those with high accuracy. Furthermore, subjects with low accuracy tend to retaliate considerably with lesser strength than that predicted by the equilibrium theory, while subjects with high accuracy tend to retaliate with more strength than that predicted by the equilibrium theory, or with strength almost equivalent to it. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2019cf1125&r=all |
| By: | S\"oren Christensen; Kristoffer Lindensj\"o |
| Abstract: | A moment constraint that limits the number of dividends in the optimal dividend problem is suggested. This leads to a new type of time-inconsistent stochastic impulse control problem. First, the optimal solution in the precommitment sense is derived. Second, the problem is formulated as an intrapersonal sequential dynamic game in line with Strotz' consistent planning. In particular, the notions of pure dividend strategies and a (strong) subgame perfect Nash equilibrium are adapted. An equilibrium is derived using a smooth fit condition. The equilibrium is shown to be strong. The uncontrolled state process is a fairly general diffusion. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.10749&r=all |
| By: | de Roos, Nicolas; Smirnov, Vladimir |
| Abstract: | We study the optimal behaviour of a cartel faced with fringe competition and imperfectly attentive consumers. Intertemporal price dispersion obfuscates consumer price comparison which aids the cartel through two channels: it reduces the effectiveness of free riding by the fringe; and it relaxes the cartel’s internal incentive constraints. Our theory explains the survival of a price-setting cartel in a homogeneous product market, provides a collusive rationale for sales and Edgeworth cycles, and characterises the cartel’s manipulation of its fringe rival through a double cut-off rule. |
| Keywords: | Collusion, fringe competition, obfuscation, price dispersion |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:syd:wpaper:2019-13&r=all |
| By: | Christian Kroer; Alexander Peysakhovich |
| Abstract: | Allocating multiple scarce items across a set of individuals is an important practical problem. In the case of divisible goods and additive preferences a convex program can be used to find the solution that maximizes Nash welfare (MNW). The MNW solution is equivalent to finding the equilibrium of a market economy (aka. the competitive equilibrium from equal incomes, CEEI) and thus has good properties such as Pareto optimality, envy-freeness, and incentive compatibility in the large. Unfortunately, this equivalence (and nice properties) breaks down for general preference classes. Motivated by real world problems such as course allocation and recommender systems we study the case of additive `at most one' (AMO) preferences - individuals want at most 1 of each item and lotteries are allowed. We show that in this case the MNW solution is still a convex program and importantly is a CEEI solution when the instance gets large but has a `low rank' structure. Thus a polynomial time algorithm can be used to scale CEEI (which is in general PPAD-hard) for AMO preferences. We examine whether the properties guaranteed in the limit hold approximately in finite samples using several real datasets. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.10925&r=all |
| By: | Shachat, Jason; Tan, Lijia |
| Abstract: | We compare two commonly used procurement English auction formats - the ex-ante reserve price and the ex-post reserve price, with symmetric and independently distributed private costs. Both formats are indirect implementations of Myerson's optimal mechanism. Both formats yield the same ex post payoffs when auctioneers optimally choose reserve prices. However, the optimal reserve prices follow two counter-intuitive prescriptions: optimal ex-ante reserve prices do not vary with the number of bidders, and optimal ex-post reserve prices are invariant to the realized auction prices. Anticipated regret, Davis et al (2011), and subjective posterior probability judgement, Shachat and Tan (2015), are two different approaches to rationalize observed auctioneers' choices that violate the two counter-intuitive prescriptions respectively. We generalized the latter model to one of Subjective Conditional Probabilities (SCP) which predicts optimal ex-ante reserve prices decreasing in the number of bidders and also predicts optimal ex-post reserve prices increasing in the realized auction prices. In our first experiment, in which costs follow a uniform distribution, we find two possible explanations to the experimental results. First, the auctioneers use the SCP model for both formats. Second, they use format-specific models. In our second experiment with a left-skewed cost distribution, we finally find that the SCP provides a unified behavioral model of how auctioneer set reserve prices in the two formats. |
| Keywords: | Procurement; English auction; ex-ante reserve price; ex-post reserve price; anticipated regret; subjective conditional probability |
| JEL: | C34 C91 D03 D44 |
| Date: | 2019–09–28 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:96225&r=all |
| By: | Schmidt, Robert J. |
| Abstract: | We propose the Point Beauty Contest, a mechanism to identify the distribution of focal points on the individual level. By contrast to conventional coordination, subjects coordinate by the distribution of points. This allows for nuanced coordination strategies, as subjects can invest in multiple alternatives at the same time and weigh their choice. A subject´s strategy choice then reveals her perception of the distribution of focal points. In an experiment on the elicitation of social norms, we compare the mechanism with conventional coordination. The data confirms the theoretical predictions regarding coordination behavior and demonstrates that the proposed technique is suited to identify the distribution of focal points on the individual level. Using Monte Carlo simulations, we find that the proposed mechanism identifies focal points on the population level more efficiently than conventional coordination. We point to the possibility of using the mechanism as a simple method to directly measure strategic uncertainty. |
| Keywords: | coordination; focal points; games theory; strategic uncertainty; social norms |
| Date: | 2019–09–27 |
| URL: | http://d.repec.org/n?u=RePEc:awi:wpaper:0667&r=all |
| By: | Schmidt, Robert J.; Schwieren, Christiane; Sproten, Alec N. |
| Abstract: | Using coordination games, we study whether social norm perception differs between inexperienced and experienced participants in economic laboratory experiments. We find substantial differences between the two groups, both regarding injunctive and descriptive social norms in the context of participation in lab experiments. By contrast, social norm perception for the context of daily life does not differ between the two groups. We therefore conclude that learning through experience is more important than selection effects for understanding differences between the two groups. We also conduct exploratory analyses on the relation between lab and field norms and find that behaving unsocial in an experiment is considered substantially more appropriate than in daily life. This appears inconsistent with the hypothesis that social preferences measured in lab experiments are inflated and indicates a distinction between revealed social preferences as measured commonly and the elicitation of normatively appropriate behavior. |
| Keywords: | laboratory experiments; selection effects; learning; generalizability; methodology |
| Date: | 2019–09–27 |
| URL: | http://d.repec.org/n?u=RePEc:awi:wpaper:0666&r=all |
| By: | Schmidt, Robert J. |
| Abstract: | We experimentally study the relationship between social norms and social preferences on the individual level. Subjects coordinate on injunctive and descriptive norms, and we test which type of norm is more strongly related to behavior in a series of dictator games. Our experiment yields three insights. First, both injunctive and descriptive norms explain dictator behavior and recipients' guesses, but perceptions about descriptive social norms are behaviorally more relevant. Second, our findings corroborate that coordination games are a valid tool to elicit social norm perception on the subject level, as the individuals´ coordination choices are good predictors for their actual behavior. Third, average descriptive norms on the population level accurately predict behavior on the population level. This suggests that the elicitation of descriptive social norms using coordination games is a potentially powerful tool to predict behavior in settings that are otherwise difficult to explore. |
| Keywords: | injunctive social norms; descriptive social norms; social preferences; coordination |
| Date: | 2019–09–27 |
| URL: | http://d.repec.org/n?u=RePEc:awi:wpaper:0668&r=all |