Game Theory
http://lists.repec.org/mailman/listinfo/nep-gth
Game Theory
2018-06-11
Revenue Guarantee Equivalence
http://d.repec.org/n?u=RePEc:cwl:cwldpp:2133&r=gth
We revisit the revenue comparison of standard auction formats, including first-price, second-price, and English auctions. We rank auctions according to their revenue guarantees, i.e., the greatest lower bound of revenue across all informational environments, where we hold fixed the distribution of bidders' values. We conclude that if we restrict attention to the symmetric affiliated models of Milgrom and Weber (1982) and monotonic pure-strategy equilibria, first-price, second-price, and English auctions all have the same revenue guarantee, which is equal to that of the first-price auction as characterized by Bergemann, Brooks, and Morris (2017a). If we consider all equilibria or if we allow more general models of information, then first-price auctions have a greater revenue guarantee than all other auctions considered.
Dirk Bergemann
Benjamin Brooks
Stephen Morris
Revenue guarantee, Common values, Affiliated values, Revenue equivalence, Revenue ranking, First-price auction, Second-price auction, English auction
2018-05
Communication with Evidence in the Lab
http://d.repec.org/n?u=RePEc:cpr:ceprdp:12927&r=gth
We study a class of sender-receiver disclosure games in the lab. Our experiment relies on a graphical representation of sender's incentives in these games, and permits partial disclosure. We use local and global properties of the incentive graph to explain behavior and performance of players across different games. Sender types whose interests are aligned with those of the receiver fully disclose, while other types use vague messages. Receivers take the evidence disclosed by senders into account, and perform better in games with an acyclic graph. Senders perform better in games with a cyclic graph. The data is largely consistent with a non-equilibrium model of strategic thinking based on the iterated elimination of obviously dominated strategies.
Hagenbach, Jeanne
Perez-Richet, Eduardo
hard evidence; information disclosure; masquerade relation; obvious dominance; Sender-receiver game; skepticism
2018-05
Solving Becker's assortative assignments and extensions
http://d.repec.org/n?u=RePEc:ewp:wpaper:376web&r=gth
We analyze assortative assignment games, introduced in Becker (1973) and Eriksson et al. (2000). We study the extreme core points and show an easy way to compute them. We find a natural solution for these games. It coincides with several well-known point solutions, the median stable utility solution (Schwarz and Yenmez, 2011) and the nucleolus (Schmeidler, 1969).We also analyze the behavior of the Shapley value. We finish with some extensions, where some hypotheses are relaxed.
F. Javier Martínez-de-Albéniz
Carlos Rafels
Neus Ybern
Assortative market, Assignment game, core, nucleolus.
2018
Compromise for the Per Capita Complaint: An Optimization Characterization of Two Equalitarian Values
http://d.repec.org/n?u=RePEc:gre:wpaper:2018-13&r=gth
The main purpose of this article is to introduce two new values for transferable utility (TU) games: the upper and lower optimal complaint values. These are based on two kinds of per capita complaint criteria and each involve a lower and upper bound of the core. In the spirit of the nucleolus, these two values are obtained by lexicographically minimizing a maximal complaint vector associated with each of the per capita complaint criterion. Interestingly, the upper and lower optimal complaint values respectively coincide with the Equal Allocation of Non-Separable Contributions and the Center-of-Gravity of Imputation Set Value for a large class of TU-games. Moreover, a characterization of these two values is achieved by invoking the equal upper and lower maximal per capita complaint properties together with efficiency.
Dongshuang Hou
Aymeric Lardon
Panfei Sun
Theo Driessen
Cooperative game, optimal complaint values, equalitarian values, equal maximal per capita complaint properties
2018-06
Identification of efficient equilibria in multiproduct trading with indivisibilities and non-monotonicity
http://d.repec.org/n?u=RePEc:dbe:wpaper:0318&r=gth
This paper focuses on multiproduct trading with indivisibilities and where a representative agent may have non-monotonic preferences. In this framework, the set of firms' profits (which comes from efficient subgame perfect Nash equilibria) is the Pareto frontier of some projection of the core of the game. We show that under monotonicity efficient subgame perfect Nash equilibria are achieved by single offers and the equilibrium characterization is easy to obtain. When dealing with non-monotonic preferences the problem becomes more challenging. Then, we define a pair of primal-dual linear programming problems that fully identifies the core of the game. A set of modified versions of the dual programming problem characterizes the Pareto-optimal frontier of the core projection on firms' coordinates. Although this approach gives us the payoff-equivalence class (Strong Nash equilibria) of all the efficient subgame perfect Nash equilibria, the number of problems to be solved may be huge.
Iván Arribas
Amparo Urbano
Multiproduct trading, Package assignment problem, Subgame perfect Nash equilibrium, Strong Nash equilibrium
2018-05
Sequential Majoritarian Blotto Games
http://d.repec.org/n?u=RePEc:ris:albaec:2018_008&r=gth
We study Colonel Blotto games with sequential battles and a majoritarian objective. For a large class of contest success functions, the equilibrium is unique and characterized by an even split: Each battle that is reached before one of the players wins a majority of battles is allocated the same amount of resources from the player's overall budget. As a consequence, a player's chance of winning any particular battle is independent of the battle field and of the number of victories and losses the player accumulated in prior battles. This result is in stark contrast to equilibrium behavior in sequential contests that do not involve either fixed budgets or a majoritarian objective. We also consider the equilibrium choice of an overall budget. For many contest success functions, if the sequence of battles is long enough the payoff structure in this extended games resembles an all-pay auction without noise.
Klumpp, Tilman
Konrad, Kai
Blotto games; dynamic battles; multi-battle contest; all-pay auctions; sequential elections
2018-05-29
Multiple Treatments with Strategic Interaction
http://d.repec.org/n?u=RePEc:arx:papers:1805.08275&r=gth
We develop an empirical framework in which we identify and estimate the effects of treatments on outcomes of interest when the treatments are the result of strategic interaction (e.g., bargaining, oligopolistic entry, peer effects). We consider a model where agents play a discrete game with complete information whose equilibrium actions (i.e., binary treatments) determine a post-game outcome in a nonseparable model with endogeneity. Due to the simultaneity in the first stage, the model as a whole is incomplete and the selection process fails to exhibit the conventional monotonicity. Without imposing parametric restrictions or large support assumptions, this poses challenges in recovering treatment parameters. To address these challenges, we first analytically characterize regions that predict equilibria in the first-stage game with possibly more than two players, and ascertain a monotonic pattern of these regions. Based on this finding, we derive bounds on the average treatment effects (ATE's) under nonparametric shape restrictions and the existence of excluded exogenous variables. We also introduce and point identify a multi-treatment version of local average treatment effects (LATE's). We apply our method to data on airlines and air pollution in cities in the U.S. We find that (i) the causal effect of each airline on pollution is positive, and (ii) the effect is increasing in the number of firms but at a decreasing rate.
Jorge Balat
Sukjin Han
2018-05
Constrained public goods in networks
http://d.repec.org/n?u=RePEc:ukc:ukcedp:1806&r=gth
This paper analyses the private provision of public goods where agents interact within a fixed network structure and may benefit only from their direct neighbours’ provisions. We survey the literature and then generalise the public goods in networks model of Bramoulle and Kranton (2007) to allow for constrained provision. In so doing, we show that, using the concept of k-insulated set, any network supports a Nash equilibrium with no intermediate contributors.
Nizar Allouch
Maia King
public goods; Nash equilibrium; k-insulated set; networks
2018-05
An Aggregative Games Approach to Merger Analysis in Multiproduct-Firm Oligopoly
http://d.repec.org/n?u=RePEc:cpr:ceprdp:12905&r=gth
Using an aggregative games approach, we analyze horizontal mergers in a model of multiproduct-firm price competition with nested CES or nested logit demands. We show that the Herfindahl index provides an adequate measure of the welfare distortions introduced by market power, and that the induced change in the naively-computed Herfindahl index is a good approximation for the market power effect of a merger. We also provide conditions under which a merger raises consumer surplus, and conditions under which a myopic, consumer-surplus-based merger approval policy is dynamically optimal. Finally, we study the aggregate surplus and external effects of a merger.
Nocke, Volker
Schutz, Nicolas
Aggregative Game; Herfindahl index; Horizontal Merger; market power; Multiproduct Firms; Oligopoly Pricing
2018-05
Mine, Ours or Yours? Unintended Framing Effects in Dictator Games
http://d.repec.org/n?u=RePEc:ces:ceswps:_7049&r=gth
This paper reports results from a classroom dictator game comparing the effects of three different sets of standard instructions. The results show that seemingly small differences in instructions induce fundamentally different perceptions regarding entitlement. Behavior is affected accordingly, i.e. instructions inducing subjects to perceive the task as distributive rather than a task of generosity lead to higher allocations to receivers (average 52% vs. 35%). A theoretical explanation integrating monetary as well as social incentives and emphasizing potential effects of uncertainty about the latter is discussed (cf. Bergh and Wichardt, 2018).
Andreas Bergh
Philipp Christoph Wichardt
dictator games, framing effects, property rights, social preferences
2018
Spillovers, Persistence and Learning: Institutions and the Dynamics of Cooperation
http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-01613850&r=gth
We study how cooperation-enforcing institutions dynamically affect values and behavior using a lab experiment designed to create individual specific histories of past institutional exposure. We show that the effect of past institutions is mostly due to " indirect " behavioral spillovers: facing penalties in the past increases partners' cooperation in the past, which in turn positively affects ones' own current behavior. We demonstrate that such indirect spillovers induce persistent effects of institutions. However, for interactions that occur early on, we find a negative effect of past enforcement due to differential learning under different enforcement institutions.
Emeric Henry
Nicolas Jacquemet
Roberto Galbiati
repeated games,persistence of institutions,Laws,social values,cooperation,learning,spillovers,experiments
2017-07-01
On Supply Function Equilibria in a Mixed Duopoly
http://d.repec.org/n?u=RePEc:ris:qmetal:2018_001&r=gth
In this paper we present a mixed duopoly model of supply function competition under uncertainty with product differentiation. We find that, regardless the nature of product heterogeneity, the best response of the private firm always arises as strategic complement. Contrary to this, state-owned firm's best response arises either as strategic complement or substitute depending on the product heterogeneity. As a result of the ex post realization of the demand uncertainty, different equilibria are reached.
Carlos, Gutiérrez-Hita
Vicente-Pérez, José
Supply Function Equilibria; Mixed oligopoly; Differentiated products
2018-05-28
Inefficiency in Private Value Bargaining with Naive Players: An Experimental Study
http://d.repec.org/n?u=RePEc:not:notcdx:2018-03&r=gth
The paper reports on an experiment on two-player double-auction bargaining with private values. We consider a setting with discrete two-point overlapping distributions of traders' valuations, in which there exists a fully efficient equilibrium. We show that if there are traders that behave naively, i.e., set bid or ask equal to their valuation, then there is no equilibrium achieving full efficiency. In the experiment, we vary the proportion of naive traders by introducing computerized players. We find that full efficiency is not achieved in the experiment with or without naive traders, and efficiency is not lower in the presence of naive traders. Subjects mostly set bid/ask prices strategically but the extent of strategic behavior is not larger in the presence of naive players. We can explain these results by a learning model of noisy strategy adjustment. We also find that framing the double auction as a direct mechanism leads to more naive behavior by experiment participants, and that allowing face-to-face pre-play communication increases efficiency although still not to the full level.
Alex Possajennikov
Rene Saran
bargaining with private values, double auction, efficiency, honesty
2018-03
Efficient and Incentive-Compatible Liver Exchange
http://d.repec.org/n?u=RePEc:boc:bocoec:951&r=gth
Liver exchange has been practiced in small numbers, mainly to overcome blood-type incom- patibility between patients and their living donors. A donor can donate either his smaller left lobe or the larger right lobe, although the former option is safer. Despite its elevated risk, right-lobe transplantation is often utilized due to size-compatibility requirement with the patient. We model liver exchange as a market-design problem, focusing on logistically simpler two-way exchanges. First, with two patient-donor sizes, we introduce an algorithm when only the safer left-lobe transplantation is feasible. We then introduce an individually rational, Pareto-efficient, and incentive-compatible mechanism that truthfully elicits the right- lobe-donation willingness of donors, and finally extend these results to a general model with any number of patient/donor sizes. The generalization requires new technical tools regarding bilateral exchanges under partial-order-induced preferences. Through simulations we show that not only liver exchange can increase the number of transplants by more than 30%, it can also increase the share of the safer left-lobe transplants.
Haluk Ergin
Tayfun Sönmez
M. Utku Ünver
Market design, liver exchange, matching, incentive compatibility, efficiency
2018-05-15
All-Pay Oligopolies: Price Competition with Unobservable Inventory Choices
http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_020_2018&r=gth
We study a class of games where stores source unobservable inventories in advance, and then simultaneously set prices. Our framework allows for firm asymmetries, heterogeneous consumer tastes, endogenous consumer information through advertising, and salvage values for unsold units. The payoff structure relates to a complete-information all-pay contest with outside options, non-monotonic winning and losing functions, and conditional investments. In the generically unique equilibrium, stores randomize their price choice and, conditional on that choice, serve all their targeted demandâ€”thus, some inventories may remain unsold. As inventory costs become fully recoverable, the equilibrium price distribution converges to an equilibrium of the associated Bertrand game (where firms first choose prices and then produce to order). This suggests that with production in advance, the choice between a Cournot analysis and a Bertrand-type analysis, as properly generalized in this paper, should depend on whether or not stores observe rivalsâ€™ inventories before setting prices.
Joao Montez
Nicolas Schutz
Oligopoly, inventories, production in advance, all-pay contests, Bertrand convergence
2018-05
An Experimental Analysis of the Complications in Colluding when Firms are Asymmetric
http://d.repec.org/n?u=RePEc:ces:ceswps:_7047&r=gth
I study an indefinitely repeated game where firms differ in size. Attempts to form cartels in such an environment, for example by rationing outputs in a manner linked to firm size differences, have generally struggled. Any successful cartel has to set production shares in a manner that ensures no firm will defect. But this can require allocating sellers disproportionate shares, which in turn makes these tacit agreements difficult to create and enforce. I analyze some experimental evidence in support of this last proposition.
Charles F. Mason
asymmetric cartel, repeated game, experiments
2018
Competition over Cursed Consumers
http://d.repec.org/n?u=RePEc:ces:ceswps:_7046&r=gth
We model firms’ quality disclosure and pricing in the presence of cursed consumers, who fail to be sufficiently skeptical about undisclosed quality. We show that neither competition nor the presence of sophisticated consumers necessarily protect cursed consumers from being exploited. Exploitation arises if markets are vertically differentiated, if there are few cursed consumers, and if average product quality is high. Three common policy measures aimed at consumer protection, i.e. mandatory disclosure, third party disclosure and consumer education may all increase exploitation and decrease welfare. Even where these policies improve overall welfare, they often lead to a reduction in consumer surplus.
Alessandro Ispano
Peter Schwardmann
naïve, cursed, disclosure, consumer protection, labeling, competition
2018
Fiscal and Monetary Regimes: A Strategic Approach
http://d.repec.org/n?u=RePEc:cpr:ceprdp:12903&r=gth
This paper develops a full-fledged strategic analysis of Wallace's "game of chicken". A public sector facing legacy nominal liabilities is comprised of fiscal and monetary authorities that respectively set the primary surplus and the price level in a non-cooperative fashion. We find that the post 2008 feature of indefinitely postponed fiscal consolidation and rapid expansion of the Federal Reserve's balance sheet is consistent with a strategic setting in which neither authority can commit to a policy beyond its current mandate, and the fiscal authority has more bargaining power than the monetary one at each date.
Barthelemy, Jean
Plantin, Guillaume
2018-05
Sweet Lemons: Mitigating Collusion in Organizations
http://d.repec.org/n?u=RePEc:rco:dpaper:100&r=gth
This paper shows that the possibility of collusion between an agent and a supervisor imposes no restrictions on the set of implementable social choice functions (SCF) and associated payoff vectors. Any SCF and any payoff profile that are implementable if the supervisor′s information was public is also implementable when this information is private and collusion is possible. To implement a given SCF we propose a one-sided mechanism that endogenously creates private information for the supervisor vis-à-vis the agent, and conditions both players′ payoffs on this endogenous information. We show that in such a mechanism all collusive side-bargaining fails, similar to the trade failure in Akerlof′s (1970) car market and in models of bilateral trade.
Pollrich, Martin
von Negenborn, Colin
mechanism design; collusion; asymmetric information; correlation;
2018-06-07
First-Price Auctions with General Information Structures: A Short Introduction
http://d.repec.org/n?u=RePEc:cwl:cwldpp:2132&r=gth
In a recent paper, [Bergemann et al. 2017a], we derive results about equilibrium behavior in the ?rst-price auction that hold across all common-prior information structures. The purpose of this letter is to give an informal introduction into the results. At the end we o?er a brief discussion of related work.
Dirk Bergemann
Benjamin Brooks
Stephen Morris
First-price auction, Information structure, Bayes correlated equilibrium, Private values, Interdependent values, Common values, Revenue, Surplus, Welfare bounds, Reserve price
2018-05
A Sequential Bargaining Model of the Fed Funds Market with Excess Reserves
http://d.repec.org/n?u=RePEc:fip:fedhwp:wp-2018-08&r=gth
We model bargaining between non-bank investors and heterogeneous bank borrowers in the federal funds market. The analysis highlights how the federal funds rate will respond to movements in other money market interest rates in an environment with elevated levels of excess reserves. The model predicts that the administered rate offered through the Federal Reserve's overnight reverse repurchase agreement facility influences the fed funds rate even when the facility is not used. Changes in repo rates pass through to the federal funds rate, but by less than one-for-one. We calibrate the model to data from 2017 and find in an out-of-sample test that the model quantitatively matches the increase in the federal funds rate in the first four months of 2018. The rise in the fed funds rate in 2018 is attributed to movements in repo rates and not to changes in the scarcity value of reserves.
Schulhofer-Wohl, Sam
Clouse, James A.
Federal funds market; federal funds rate; Federal Reserve; interest rates; money market
2018-05-01
Cryptocurrency Equilibria Through Game Theoretic Optimization
http://d.repec.org/n?u=RePEc:arx:papers:1805.10128&r=gth
Optimization methods are used to determine equilibria of investment in cryptocurrencies. The basic assumptions involve existence of a core group (the "wealthy") that fears the loss of substantial assets through government seizure. Speculators constitute another group that tends to introduce volatility and risk for the wealthy. The wealthy must divide their assets between the home currency and the cryptocurrency, while the government decides on the probability of seizing a fraction the assets of this group. Under the assumption that each group exhibits risk aversion through a utility function, we establish the existence and uniqueness of Nash equilibrium. Also examined is the more realistic optimization problem in which the government policy cannot be reversed, while the wealthy can adjust their allocation in reaction to the government's designation of probability. The methodology leads to an understanding the equilibrium market capitalization of cryptocurrencies.
Carey Caginalp
Gunduz Caginalp
2018-05
Interactive Information Design
http://d.repec.org/n?u=RePEc:hal:psewpa:halshs-01791918&r=gth
Westudytheinteractionbetweenmultipleinformationdesignerswho trytoinfluencethebehavior ofasetofagents.Whenthesetofmessagesavailabletoeachdesignerisfinite,suchgamesalways admitsubgameperfectequilibria.Whendesignersproducepublicinformationaboutindependent piecesofinformation,everyequilibriumofthedirectgame(inwhichthe setofmessagescoincides withthesetofstates)isanequilibriumwithlarger(possiblyinfinite)messagesets.Theconverse is trueforaclassofMarkovianequilibriaonly.Whendesignersproduce informationfortheirown corporationofagents,purestrategyequilibriaexistandarecharacterizedviaanauxiliarynormal formgame.Inaninfinite-horizonmulti-periodextensionofinformationdesigngames,afeasible outcomewhichParetodominatesamoreinformativeequilibriumofthe one-periodgameissupported byanequilibriumofthemulti-periodgame.
Frédéric Koessler
Marie Laclau
Tristan Tomala
Bayesian persuasion,information design,sharing rules,splitting games,statistical experiments
2018-05
A Qualitative Theory of Conflict Resolution and Political Compromise
http://d.repec.org/n?u=RePEc:hal:cesptp:hal-01796062&r=gth
We view political activity as an interaction between forces seeking to achieve a political agenda. The viability of a situation depends on the compatibility of such agendas. However even in a conflictual situation a compromise may be possible. Mathematically a political structure is modeled as a simplicial complex and a viable configuration as a simplex. A represented compromise is a viable configuration obtained by the withdrawal of some agents in favor of some friendly representatives. A delegated compromise is a sophisticated version of a compromise obtained by the iteration of the withdrawal process. Existence of such solutions depends on the discrete topology of the simplicial complex. In particular we prove that the existence of a delegated compromise is equivalent to the strong contractibility of the simplicial complex.
Joseph Abdou
Hans Keiding
Delegation, compromise, simplicial complex, contiguity,strong homotopy
2018-05-19
The Unilateral Accident Model under a Constrained Cournot-Nash Duopoly
http://d.repec.org/n?u=RePEc:gre:wpaper:2018-14&r=gth
This paper extends the basic unilateral accident model to allow for Cournot competition. Two firms compete with production input and prevention as strategic variables under asymmetric capacity constraints. We find that liability regimes exert a crucial influence on the equilibrium price and outputs. Strict liability leads to higher output and higher risk compared to negligence. We also study the conditions under which both regimes converge.
Gérard Mondello
Evens Salies
Tort Law, Strict Liability, Negligence Rule, Imperfect Competition, Oligopoly, Cournot Competition
2018-06