1,721,044 research outputs found
Introduzione a "Ritorni Medievali. Europa e Oriente nella reinvenzione moderna dell'Età di mezzo"
No full textLearning dynamics in limited-control repeated games
No full textIn imperfect-information games, a common assumption is that players can perfectly model the strategic interaction and always maintain control over their decision points. We relax this assumption by introducing the notion of limited-control repeated games. In this setting, two players repeatedly play a zero-sum extensive-form game and, at each iteration, a player may lose control over portions of her game tree. Intuitively, this can be seen as the chance player hijacking the interaction and taking control of certain decision points. What subsequently happens is no longer controllable-or even known-by the original players. We introduce pruned fictitious play, a variation of fictitious play that can be employed by the players to reach an equilibrium in limited-control repeated games. We motivate this technique with the notion of limited best response, which is the key step of the learning rule we employ. We provide a general result on the probabilistic guarantees of a limited best response with respect to the original game model. Then, we experimentally evaluate our technique and show that pruned fictitious play has good convergence properties
Computing Optimal Ex Ante Correlated Equilibria in Two-Player Sequential Games
No full textNo abstract availabl
Persuading Voters: It's Easy to Whisper, It's Hard to Speak Loud
Full text linkWe focus on the following natural question: is it possible to influence the outcome of a voting process through the strategic provision of information to voters who update their beliefs rationally? We investigate whether it is computationally tractable to design a signaling scheme maximizing the probability with which the sender's preferred candidate is elected. We resort to the model recently introduced by Arieli and Babichenko (2019) (i.e., without inter-agent externalities), and focus on, as illustrative examples, k-voting rules and plurality voting. There is a sharp contrast between the case in which private signals are allowed and the more restrictive setting in which only public signals are allowed. In the former, we show that an optimal signaling scheme can be computed efficiently both under a k-voting rule and plurality voting. In establishing these results, we provide two contributions applicable to general settings beyond voting. Specifically, we extend a well-known result by Dughmi and Xu (2017) to more general settings and prove that, when the sender's utility function is anonymous, computing an optimal signaling scheme is fixed-parameter tractable in the number of receivers' actions. In the public signaling case, we show that the sender's optimal expected return cannot be approximated to within any factor under a k-voting rule. This negative result easily extends to plurality voting and problems where utility functions are anonymous
Private Bayesian persuasion with sequential games
No full textWe study an information-structure design problem (a.k.a. a persuasion problem) with a single sender and multiple receivers with actions of a priori unknown types, independently drawn from action-specific marginal probability distributions. As in the standard Bayesian persuasion model, the sender has access to additional information regarding the action types, which she can exploit when committing to a (noisy) signaling scheme through which she sends a private signal to each receiver. The novelty of our model is in considering the much more expressive case in which the receivers interact in a sequential game with imperfect information, with utilities depending on the game outcome and the realized action types. After formalizing the notions of ex ante and ex interim persuasiveness (which differ by the time at which the receivers commit to following the sender’s signaling scheme), we investigate the continuous optimization problem of computing a signaling scheme which maximizes the sender’s expected revenue. We show that computing an optimal ex ante persuasive signaling scheme is NP-hard when there are three or more receivers. Instead, in contrast with previous hardness results for ex interim persuasion, we show that, for games with two receivers, an optimal ex ante persuasive signaling scheme can be computed in polynomial time thanks to the novel algorithm we propose, based on the ellipsoid method
Private Bayesian Persuasion with Sequential Games
No full textWe study an information-structure design problem (a.k.a. a persuasion problem) with a single sender and multiple receivers with actions of a priori unknown types, independently drawn from action-specific marginal probability distributions. As in the standard Bayesian persuasion model, the sender has access to additional information regarding the action types, which she can exploit when committing to a (noisy) signaling scheme through which she sends a private signal to each receiver. The novelty of our model is in considering the much more expressive case in which the receivers interact in a sequential game with imperfect information, with utilities depending on the game outcome and the realized action types. After formalizing the notions of ex ante and ex interim persuasiveness (which differ by the time at which the receivers commit to following the sender's signaling scheme), we investigate the continuous optimization problem of computing a signaling scheme which maximizes the sender's expected revenue. We show that computing an optimal ex ante persuasive signaling scheme is NP-hard when there are three or more receivers. Instead, in contrast with previous hardness results for ex interim persuasion, we show that, for games with two receivers, an optimal ex ante persuasive signaling scheme can be computed in polynomial time thanks to the novel algorithm we propose, based on the ellipsoid method
Computational Results for Extensive-Form Adversarial Team Games
Full text linkWe provide, to the best of our knowledge, the first computational study of extensive-form adversarial team games. These games are sequential, zero-sum games in which a team of players, sharing the same utility function, faces an adversary. We define three different scenarios according to the communication capabilities of the team. In the first, the teammates can communicate and correlate their actions both before and during the play. In the second, they can only communicate before the play. In the third, no communication is possible at all. We define the most suitable solution concepts, and we study the inefficiency caused by partial or null communication, showing that the inefficiency can be arbitrarily large in the size of the game tree. Furthermore, we study the computational complexity of the equilibrium-finding problem in the three scenarios mentioned above, and we provide, for each of the three scenarios, an exact algorithm. Finally, we empirically evaluate the scalability of the algorithms in random games and the inefficiency caused by partial or null communication
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