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on Game Theory |
| By: | Ngo Van Long |
| Abstract: | This paper defines the concept of feedback Kant-Nash equilibrium for a discrete-time model of resource exploitation by infinitely-lived Kantian and Nashian players, where we define Kantian agents as those who act in accordance with the categorical imperative. We revisit a well-known dynamic model of the tragedy of the commons and ask what would happen if not all agents are solely motivated by self interest. We establish that even without external punishment of violation of social norms, if a sufficiently large fraction of the population consists of Kantian agents, the tragedy of the commons can be substantially mitigated. |
| Keywords: | Kantian equilibrium, rule of behavior, categorical imperative |
| JEL: | C71 D62 D71 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_7729&r=all |
| By: | Hans Carlsson; Philipp Christoph Wichardt |
| Abstract: | This paper proposes a comprehensive perspective on the question of self-enforcing solutions for normal form games. While this question has been widely discussed in the literature, the focus is usually either on strict incentives for players to stay within the proposed solution or on strategic uncertainty, i.e. robustness to trembles. The present approach combines both requirements in proposing the concept of robust sets, i.e. sets of strategy profiles which satisfy both strict incentives and robustness to strategic uncertainty. The result is a set valued solution, a variant of which is shown to exist for all finite normal form games. |
| Keywords: | game theory, self-enforcing solution, strict incentives, strategic uncertainty |
| JEL: | C72 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_7715&r=all |
| By: | Bettina Klaus; Alexandru Nichifor |
| Abstract: | We propose a new set of mechanisms, which we call serial dictatorship mechanisms with individual reservation prices for the allocation of homogeneous indivisible objects, e.g., specialist clinic appointments. We show that a mechanism ' satis es minimal tradability,individual rationality, strategy-proofness, consistency, independence of unallocated objects, and non wasteful tie-breaking if and only if there exists a reservation price vector r and a priority ordering such that ' is a serial dictatorship mechanism with reservation prices based on r and . We obtain a second characterization by replacing individual rationality with non-imposition. In both our characterizations r, , and 'are all found simultaneously and endogenously from the properties. Finally, we illustrate how our model, mechanism, and results, capture the normative requirements governing the functioning of some real life markets and the mechanisms that these markets use. |
| Keywords: | serial dictatorship; individual reservation prices; strategy-proofness; consistency. |
| JEL: | C78 D71 |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:lau:crdeep:19.04&r=all |
| By: | Tatsuhiro Shichijo |
| Abstract: | We theoretically study the effect of a third person enforcement on a one-shot prisoner's dilemma game played by two persons, with whom the third person plays repeated prisoner's dilemma games. We find that the possibility of the third person's future punishment causes them to cooperate in the one-shot game. |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1908.04971&r=all |
| By: | Ata Atay; Pedro Calleja; Sergio Soteras |
| Abstract: | This paper takes a game theoretical approach to open shop scheduling problems with unit execution times to minimize the sum of completion times. By supposing an initial schedule and associating each job (consisting in a number of operations) to a different player, we can construct a cooperative TU-game associated with any open shop scheduling problem. We assign to each coalition the maximal cost savings it can obtain through admissible rearrangements of jobs' operations. By providing a core allocation, we show that the associated games are balanced. Finally, we relax the definition of admissible rearrangements for a coalition to study to what extend balancedness still holds. |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1907.12909&r=all |
| By: | Rodrigo A. Velez; Alexander L. Brown |
| Abstract: | We study the plausibility of sub-optimal Nash equilibria of the direct revelation mechanism associated with a strategy-proof social choice function. By using the recently introduced empirical equilibrium analysis (Velez and Brown, 2019, arXiv:1804.07986) we determine that this behavior is plausible only when the social choice function violates a non-bossiness condition and information is not interior. Analysis of the accumulated experimental and empirical evidence on these games supports our findings. |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1907.12408&r=all |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Philipp Strack (Cowles Foundation, Yale University) |
| Abstract: | A single seller faces a sequence of buyers with unit demand. The buyers are forward-looking and long-lived but vanish (and are replaced) at a constant rate. The arrival time and the valuation is private information of each buyer and unobservable to the seller. Any incentive-compatible mechanism has to induce truth-telling about the arrival time and the evolution of the valuation. We derive the optimal stationary mechanism, characterize its qualitative structure and derive a closed-form solution. As the arrival time is private information, the agent can choose the time at which he reports his arrival. The truth-telling constraint regarding the arrival time can be represented as an optimal stopping problem. The stopping time determines the time at which the agent decides to participate in the mechanism. The resulting value function of each agent can not be too convex and has to be continuously differentiable everywhere, reflecting the option value of delaying participation. The optimal mechanism thus induces progressive participation by each agent: he participates either immediately or at a future random time. |
| Keywords: | Dynamic Mechanism Design, Observable Arrival, Unobservable Arrival, Repeated Sales, Interim Incentive Constraints, Interim Participation Constraints, Stopping Problem, Option Value, Progressive Participation |
| JEL: | D44 D82 D83 |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2189&r=all |
| By: | Bizzotto, Jacopo; Perez-Richet, Eduardo; Vigier, Adrien |
| Abstract: | We consider a general information design problem in which the task of producing information is delegated to an agent who can privately choose between the procedure designed by the principal and a default procedure. Procedures are constrained as to which messages they use, and possibly how they may be used. The principal can incentivize the agent via transfers conditioned on messages. This gives rise to a moral hazard problem in which the principal faces a trade-off between generating information that is persuasive in the continuation game, or generating information about the choice of the agent so as to lower the cost of agency. We provide a general methodology to solve such problems, and characterize an optimal procedure. We apply our results to information acquisition and persuasion examples. |
| Keywords: | Agency Cost; Information Acquisition; information design; moral hazard |
| JEL: | C72 D82 |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:13868&r=all |
| By: | Daniela Glätzle-Rützler; Philipp Lergetporer; Matthias Sutter |
| Abstract: | Many important intertemporal decisions, such as investments of firms or households, are made by groups rather than individuals. Little is known what happens to such collective decisions when group members have different incentives for waiting, because the economics literature on group decision making has, so far, assumed homogeneity within groups. In a lab experiment, we study the causal effect of group members’ heterogeneous payoffs from waiting on intertemporal choices. We find that three-person groups behave more patiently than individuals and that this effect is driven by the presence of at least one group member with a high payoff from waiting. We present group chat content, survey data, and additional treatments to uncover the mechanism through which heterogeneity in groups increases patience. |
| Keywords: | patience, time preferences, group decisions, payoff heterogeneity, experiment |
| JEL: | C91 C92 D03 D90 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_7716&r=all |
| By: | de Clippel, Geoffroy; Eliaz, Kfir; Fershtman, Daniel; Rozen, Kareen |
| Abstract: | Each period, a principal must assign one of two agents to some task. Profit is stochastically higher when the agent is qualified for the task. The principal cannot observe qualification. Her only decision is which of the two agents to assign, if any, given the public history of selections and profits. She cannot commit to any rule. While she maximizes expected discounted profits, each agent maximizes his expected discounted selection probabilities. We fully characterize when the principal's first-best payoff is attainable in equilibrium, and identify a simple strategy profile achieving this first-best whenever feasible. We propose a new refinement for dynamic mechanisms (without transfers) where the designer is a player, under which we show the principal's next-best, when the first-best is unachievable, is the one-shot Nash. We show how our analysis extends to variations on the game accommodating more agents, caring about one's own performance, cheap talk and losses. |
| Keywords: | dynamic allocation; mechanism design without commitment; mechanism design without transfers |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:13891&r=all |
| By: | Dubovik, Andrei |
| Abstract: | I study mergers where each firm owns multiple shops across a country. Presently, the European Commission views every shop, together with the shops from its catchment area, as an isolated market. Such an approach is internally inconsistent. I show how to extend the European Commission's approach to consistently take overlaps in catchment areas into account. My model is a specialization of the existing network theory that is aimed to be feasible in real merger cases. As a demonstration, I study a past merger case and I find that neglecting overlaps in catchment areas can result in substantial biases. |
| Keywords: | mergers, networks, spatial competition, consumer demand |
| JEL: | D43 D85 L13 L14 L40 |
| Date: | 2018–06–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:95458&r=all |
| By: | Frank Bosserhoff; Mitja Stadje |
| Abstract: | We consider a time-consistent mean-variance portfolio selection problem of an insurer and allow for the incorporation of basis (mortality) risk. The optimal solution is identified with a Nash subgame perfect equilibrium. We characterize an optimal strategy as solution of a system of partial integro-differential equations (PIDEs), a so called extended Hamilton-Jacobi-Bellman (HJB) system. We prove that the equilibrium is necessarily a solution of the extended HJB system. Under certain conditions we obtain an explicit solution to the extended HJB system and provide the optimal trading strategies in closed-form. A simulation shows that the previously found strategies yield payoffs whose expectations and variances are robust regarding the distribution of jump sizes of the stock. The same phenomenon is observed when the variance is correctly estimated, but erroneously ascribed to the diffusion components solely. Further, we show that differences in the insurance horizon and the time to maturity of a longevity asset do not add to the variance of the terminal wealth. |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1908.05534&r=all |
| By: | Allan Borodin; Akash Rakheja |
| Abstract: | We discuss the problem of setting prices in an electronic market that has more than one buyer. We assume that there are self-interested sellers each selling a distinct item that has an associated cost. Each buyer has a submodular valuation for purchasing any subset of items. The goal of the sellers is to set a price for their item such that their profit from possibly selling their item to the buyers is maximized. Our most comprehensive results concern a multi copy setting where each seller has m copies of their item and there are m buyers. In this setting, we give a necessary and sufficient condition for the existence of market clearing pure Nash equilibrium. We also show that not all equilibria are market clearing even when this condition is satisfied contrary to what was shown in the case of a single buyer in [2]. Finally, we investigate the pricing problem for multiple buyers in the limited supply setting when each seller only has a single copy of their item. |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1907.11915&r=all |
| By: | David Rushing Dewhurst; Christopher M. Danforth; Peter Sheridan Dodds |
| Abstract: | Foreign power interference in domestic elections is an age-old, existential threat to societies. Manifested through myriad methods from war to words, such interference is a timely example of strategic interaction between economic and political agents. We model this interaction between rational game players as a continuous-time differential game, constructing an analytical model of this competition with a variety of payoff structures. Structures corresponding to all-or-nothing attitudes regarding the effect of the interference operations by only one player lead to an arms race in which both countries spend increasing amounts on interference and counter-interference operations. We then confront our model with data pertaining to the Russian interference in the 2016 United States presidential election contest, introducing and estimating a Bayesian structural time series model of election polls and social media posts by Russian internet trolls. We show that our analytical model, while purposefully abstract and simple, adequately captures many temporal characteristics of the election and social media activity. |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1908.02793&r=all |
| By: | Matthew Gould; Matthew D. Rablen |
| Abstract: | We focus on the preferences of an extremely salient group of highly-experienced individuals who are entrusted with making decisions that affect the lives of millions of their citizens, heads of government. We test for the presence of a fundamental behavioral bias, loss aversion, in the way heads of government choose decision rules for international organizations. If loss aversion disappears with experience and high-stakes it should not exhibited in this context. Loss averse leaders choose decision rules that oversupply negative (blocking) power at the expense of positive power (to initiate affirmative action), causing welfare losses through harmful policy persistence and reform deadlocks. We find evidence of significant loss aversion (λ = 4:4) in the Qualified Majority rule in the Treaty of Lisbon, when understood as a Nash bargaining outcome. World leaders may be more loss averse than the populous they represent. |
| Keywords: | loss aversion, behavioral biases, constitutional design, voting, bargaining, voting power, EU Council of Ministers |
| JEL: | D03 D81 D72 C78 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_7763&r=all |
| By: | Battaglini, Marco; Patacchini, Eleonora; Rainone, Edoardo |
| Abstract: | We present a model of the U.S. Congress in which social connections among Congress members are endogenous and matter for their legislative activity. We propose a novel equilibrium concept for the network formation game that allows for a sharp characterization of equilibrium behavior and that yields a unique prediction under testable conditions. While the equilibrium is characterized by a large number of nonlinear equations, we show that the model can be structurally estimated by an appropriately designed Approximate Bayesian Computation method. Estimating the model using data from the 109th to 113th U.S. Congresses, we show that social connections are important for legislators' productivities and we identify some of the key determinants of social centralities in Congress. |
| JEL: | D71 D72 |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:13845&r=all |