490 research outputs found
On some further properties of nonzero-sum diffential games
Optimality principle and open loop-closed loop control relations in nonzero-sum differential game
Multistage communication with and without verifiable types
We survey the main results on strategic information transmission, which is often referred to as ``persuasion" when types are verifiable and as ``cheap talk" when they are not. In the simplest ``cheap talk'' model, an informed player sends a single message to a receiver who makes a decision. The players' utilities depend on the sender's information and the receiver's decision, but not on the sender's message. Furthermore, the messages that are available to the sender do not depend on his true information. As is well-known, such a unilateral ``cheap talk" can affect the sender's decision at equilibrium. In a more general model, both players can exchange simultaneous costless messages during several stages before the final decision. The utility functions are unchanged. Multistage conversation allows the players to reach more equilibrium outcomes, which possibly Pareto dominate the original ones. More precisely, the set of equilibrium outcomes of long cheap talk games is fully characterized; it increases with the number of communication stages and can become even larger if no deadline is imposed. Concentrating on cheap talk is not appropriate if the informed player can influence the decision maker by producing unfalsifiable documents. In order to capture this possibility formally, one assumes that the informed player's set of messages depends on his private information. The literature has mostly dealt with unilateral persuasion. But multistage, bilateral communication enables the players to reach more equilibrium outcomes in the case of verifiable types as in the case of unverifiable ones. Equilibria of long persuasion games are fully characterized when information can be certified at any precision level.Cheap talk; certification; incomplete information; information transmission; jointly controlled lotteries; verifiable types
Correlated equilibria and communication in games.
Analyse bayésienne; Théorie des jeux; Information privée;
Recursive Inspection Games
We consider a sequential inspection game where an inspector uses a limited
number of inspections over a larger number of time periods to detect a
violation (an illegal act) of an inspectee. Compared with earlier models, we
allow varying rewards to the inspectee for successful violations. As one
possible example, the most valuable reward may be the completion of a sequence
of thefts of nuclear material needed to build a nuclear bomb. The inspectee can
observe the inspector, but the inspector can only determine if a violation
happens during a stage where he inspects, which terminates the game; otherwise
the game continues. Under reasonable assumptions for the payoffs, the
inspector's strategy is independent of the number of successful violations.
This allows to apply a recursive description of the game, even though this
normally assumes fully informed players after each stage. The resulting
recursive equation in three variables for the equilibrium payoff of the game,
which generalizes several other known equations of this kind, is solved
explicitly in terms of sums of binomial coefficients. We also extend this
approach to non-zero-sum games and, similar to Maschler (1966), "inspector
leadership" where the inspector commits to (the same) randomized inspection
schedule, but the inspectee acts legally (rather than mixes as in the
simultaneous game) as long as inspections remain.Comment: final version for Mathematics of Operations Research, new Theorem
On values of repeated games with signals
We study the existence of different notions of value in two-person zero-sum
repeated games where the state evolves and players receive signals. We provide
some examples showing that the limsup value (and the uniform value) may not
exist in general. Then we show the existence of the value for any Borel payoff
function if the players observe a public signal including the actions played.
We also prove two other positive results without assumptions on the signaling
structure: the existence of the value in any game and the existence of
the uniform value in recursive games with nonnegative payoffs.Comment: Published at http://dx.doi.org/10.1214/14-AAP1095 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Improving Efficiency and Scalability of Sum of Squares Optimization: Recent Advances and Limitations
It is well-known that any sum of squares (SOS) program can be cast as a
semidefinite program (SDP) of a particular structure and that therein lies the
computational bottleneck for SOS programs, as the SDPs generated by this
procedure are large and costly to solve when the polynomials involved in the
SOS programs have a large number of variables and degree. In this paper, we
review SOS optimization techniques and present two new methods for improving
their computational efficiency. The first method leverages the sparsity of the
underlying SDP to obtain computational speed-ups. Further improvements can be
obtained if the coefficients of the polynomials that describe the problem have
a particular sparsity pattern, called chordal sparsity. The second method
bypasses semidefinite programming altogether and relies instead on solving a
sequence of more tractable convex programs, namely linear and second order cone
programs. This opens up the question as to how well one can approximate the
cone of SOS polynomials by second order representable cones. In the last part
of the paper, we present some recent negative results related to this question.Comment: Tutorial for CDC 201
Nonzero-sum differential games - Concepts and models
Differential games controlling inputs to single dynamic system as extension of optimal control theor
Long Persuasion Games
This paper characterizes geometrically the set of all Nash equilibrium payoffs achievable with unmediated communication in persuasion games, i.e., games with an informed expert and an uninformed decisionmaker in which the expert's information is certifiable. The first equilibrium characterization is provided for unilateral persuasion games, and the second for multistage, bilateral persuasion games. As in Aumann and Hart (2003), we use the concepts of diconvexification and dimartingale. A leading example illustrates both geometric characterizations and shows how the expert, whatever his type, can increase his equilibrium payoff compared to all equilibria of the unilateral persuasion game by delaying information certification.cheap talk, communication, diconvexification, dimartingale, disclosure of certifiable information, jointly controlled lotteries, long conversation, persuasion, verifiable types
Nondominated equilibrium solutions of multiobjective two-person nonzero-sum games in normal and extensive forms
In this paper, we review the development of studies
on multiobjective noncooperative games, and particularly we
focus on nondominated equilibrium solutions in multiobjective two-person nonzero-sum games in normal and extensive forms.
After outlining studies related to multiobjective noncooperative games, we treat multiobjective two-person nonzero-sum games in normal form, and a mathematical programming problem yielding nondominated equilibrium solutions is shown. As for extensive form games, we first provide a game representation of the sequence form, and then formulate a mathematical programming problem for obtaining nondominated equilibrium solutions
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