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on Game Theory |
| By: | Chi, Chang Koo; Murto, Pauli; Valimaki, Juuso |
| Abstract: | This paper analyzes all-pay auctions where the bidders have affiliated values for the object for sale and where the signals take binary values. Since signals are correlated, high signals indicate a high degree of competition in the auction and since even losing bidders must pay their bid, non-monotonic equilibria arise. We show that the game has a unique symmetric equilibrium, and that whenever the equilibrium is non-monotonic the contestants earn no rents. All-pay auctions result in low expected rents to the bidders, but also induce inefficient allocations in models with affiliated private values. With two bidders, the effect on rent extraction dominates, and all-pay auction outperforms standard auctions in terms of expected revenue. With many bidders, this revenue ranking is reversed for some parameter values and the inefficient allocations persist even in large auctions. |
| Keywords: | All-Pay Auctions, Affiliated Signals, Common Values |
| JEL: | D44 D82 |
| Date: | 2017–06–17 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:80799&r=gth |
| By: | Martimort, David; Semenov, Aggey; Stole, Lars |
| Abstract: | We characterize the complete set of equilibrium allocations to an intrinsic common agency screening game as the set of solutions to self-generating optimization programs. We provide a complete characterization of equilibrium outcomes for regular environments by relying on techniques developed elsewhere for aggregate games and for the mechanism design delegation literature. The set of equilibria include those with non-differentiable payoffs and discontinuous choices, as well as equilibria that are smooth and continuous in types. We identify one equilibrium, the maximal equilibrium, which is the unique solution to a self-generating optimization program with the largest (or “maximal”) domain, and the only equilibrium that is supported with bi-conjugate (i.e., least-concave) tariffs. The maximal equilibrium exhibits a n-fold distortion caused by each of the n principal’s non-cooperative behavior in over- harvesting the agent’s information rent. Furthermore, in any equilibrium, over any interval of types in which there is full separation, the agent’s equilibrium action corresponds to the allocation in the maximal equilibrium. Under mild conditions, the maximal equilibrium maximizes the agent’s information rent within the class of equilibrium allocations. When the principals’ most-preferred equilibrium allocation differs from the maximal equilibrium, we demonstrate that the agent’s choice function exhibits an interval of bunching over the worst agent types, and elsewhere corresponds with the maximal allocation. The optimal region of bunching trades off the principals’ desire to constrain inefficient n-fold marginalizations of the agent’s rent against the inefficiency of pooling agent types. |
| Keywords: | Intrinsic common agency, aggregate games, mechanism design for delegated decision-making, duality, equilibrium selection. |
| JEL: | D82 D86 |
| Date: | 2017–08–16 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:80870&r=gth |
| By: | Ali Hussein Samadi; Afshin Montakhab; Hussein Marzban; Sakine Owjimehr |
| Abstract: | Classical game theory addresses decision problems in multi-agent environment where one rational agent's decision affects other agents' payoffs. Game theory has widespread application in economic, social and biological sciences. In recent years quantum versions of classical games have been proposed and studied. In this paper, we consider a quantum version of the classical Barro-Gordon game which captures the problem of time inconsistency in monetary economics. Such time inconsistency refers to the temptation of weak policy maker to implement high inflation when the public expects low inflation. The inconsistency arises when the public punishes the weak policy maker in the next cycle. We first present a quantum version of the Barro-Gordon game. Next, we show that in a particular case of the quantum game, time-consistent Nash equilibrium could be achieved when public expects low inflation, thus resolving the game. |
| Date: | 2017–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1708.05689&r=gth |
| By: | Christoph Aymanns; Jakob Foerster; Co-Pierre Georg |
| Abstract: | We model the spread of news as a social learning game on a network. Agents can either endorse or oppose a claim made in a piece of news, which itself may be either true or false. Agents base their decision on a private signal and their neighbors' past actions. Given these inputs, agents follow strategies derived via multi-agent deep reinforcement learning and receive utility from acting in accordance with the veracity of claims. Our framework yields strategies with agent utility close to a theoretical, Bayes optimal benchmark, while remaining flexible to model re-specification. Optimized strategies allow agents to correctly identify most false claims, when all agents receive unbiased private signals. However, an adversary's attempt to spread fake news by targeting a subset of agents with a biased private signal can be successful. Even more so when the adversary has information about agents' network position or private signal. When agents are aware of the presence of an adversary they re-optimize their strategies in the training stage and the adversary's attack is less effective. Hence, exposing agents to the possibility of fake news can be an effective way to curtail the spread of fake news in social networks. Our results also highlight that information about the users' private beliefs and their social network structure can be extremely valuable to adversaries and should be well protected. |
| Date: | 2017–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1708.06233&r=gth |
| By: | Finn Christensen (Department of Economics, Towson University) |
| Abstract: | Under regularity and boundary conditions which ensure an interior maximum, I show that there is a unique critical point which is a global maximum if and only if the Hessian determinant of the negated objective function is strictly positive at any critical point. Within the large class of Morse functions, and subject to boundary conditions, this local and ordinal condition generalizes strict concavity, and is satisfied by nearly all strictly quasiconcave functions. The result also provides a new uniqueness theorem for potential games. |
| Keywords: | optimization, index theory, potential games. |
| JEL: | C02 C72 |
| Date: | 2017–08 |
| URL: | http://d.repec.org/n?u=RePEc:tow:wpaper:2017-04&r=gth |
| By: | James Costain (Banco de España) |
| Abstract: | This paper models a near-rational agent who chooses from a set of feasible alternatives, subject to a cost function for precise decision-making. Unlike previous papers in the «control costs» tradition, here the cost of decisions is explicitly interpreted in terms of time. That is, by choosing more slowly, the decision-maker can achieve greater accuracy. Moreover, the timing of the choice is itself also treated as a costly decision. A trade off between the precision and the speed of choice becomes especially interesting in a strategic situation, where each decision maker must react to the choices of others. Here, the model of costly choice is applied to a sequential bargaining game. The game closely resembles that of Perry and Reny (1993), in which making an offer, or reacting to an offer, requires a positive amount of time. But whereas Perry and Reny treat the decision time as an exogenous fixed cost, here we allow the decision-maker to vary precision by choosing more or less quickly, thus endogenizing the order and timing of offers and responses in the game. Numerical simulations of bargaining equilibria closely resemble those of the Binmore, Rubinstein, and Wolinsky (1983) framework, except that the time to reach agreement is nonzero and offers are sometimes rejected. In contrast to the model of Perry and Reny, our numerical results indicate that equilibrium is unique when the space of possible offers is sufficiently finely spaced. |
| Keywords: | C72, C78, D81 |
| Date: | 2017–08 |
| URL: | http://d.repec.org/n?u=RePEc:bde:wpaper:1729&r=gth |