12,126 research outputs found
A Continuation Method for Nash Equilibria in Structured Games
Structured game representations have recently attracted interest as models
for multi-agent artificial intelligence scenarios, with rational behavior most
commonly characterized by Nash equilibria. This paper presents efficient, exact
algorithms for computing Nash equilibria in structured game representations,
including both graphical games and multi-agent influence diagrams (MAIDs). The
algorithms are derived from a continuation method for normal-form and
extensive-form games due to Govindan and Wilson; they follow a trajectory
through a space of perturbed games and their equilibria, exploiting game
structure through fast computation of the Jacobian of the payoff function. They
are theoretically guaranteed to find at least one equilibrium of the game, and
may find more. Our approach provides the first efficient algorithm for
computing exact equilibria in graphical games with arbitrary topology, and the
first algorithm to exploit fine-grained structural properties of MAIDs.
Experimental results are presented demonstrating the effectiveness of the
algorithms and comparing them to predecessors. The running time of the
graphical game algorithm is similar to, and often better than, the running time
of previous approximate algorithms. The algorithm for MAIDs can effectively
solve games that are much larger than those solvable by previous methods
Computational Results for Extensive-Form Adversarial Team Games
We 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
Quasi-Perfect Stackelberg Equilibrium
Equilibrium refinements are important in extensive-form (i.e., tree-form)
games, where they amend weaknesses of the Nash equilibrium concept by requiring
sequential rationality and other beneficial properties. One of the most
attractive refinement concepts is quasi-perfect equilibrium. While
quasi-perfection has been studied in extensive-form games, it is poorly
understood in Stackelberg settings---that is, settings where a leader can
commit to a strategy---which are important for modeling, for example, security
games. In this paper, we introduce the axiomatic definition of quasi-perfect
Stackelberg equilibrium. We develop a broad class of game perturbation schemes
that lead to them in the limit. Our class of perturbation schemes strictly
generalizes prior perturbation schemes introduced for the computation of
(non-Stackelberg) quasi-perfect equilibria. Based on our perturbation schemes,
we develop a branch-and-bound algorithm for computing a quasi-perfect
Stackelberg equilibrium. It leverages a perturbed variant of the linear program
for computing a Stackelberg extensive-form correlated equilibrium. Experiments
show that our algorithm can be used to find an approximate quasi-perfect
Stackelberg equilibrium in games with thousands of nodes
Robust Stackelberg Equilibria in Extensive-Form Games and Extension to Limited Lookahead
Stackelberg equilibria have become increasingly important as a solution
concept in computational game theory, largely inspired by practical problems
such as security settings. In practice, however, there is typically uncertainty
regarding the model about the opponent. This paper is, to our knowledge, the
first to investigate Stackelberg equilibria under uncertainty in extensive-form
games, one of the broadest classes of game. We introduce robust Stackelberg
equilibria, where the uncertainty is about the opponent's payoffs, as well as
ones where the opponent has limited lookahead and the uncertainty is about the
opponent's node evaluation function. We develop a new mixed-integer program for
the deterministic limited-lookahead setting. We then extend the program to the
robust setting for Stackelberg equilibrium under unlimited and under limited
lookahead by the opponent. We show that for the specific case of interval
uncertainty about the opponent's payoffs (or about the opponent's node
evaluations in the case of limited lookahead), robust Stackelberg equilibria
can be computed with a mixed-integer program that is of the same asymptotic
size as that for the deterministic setting.Comment: Published at AAAI1
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