640 research outputs found
Computation of Stackelberg Equilibria of Finite Sequential Games
The Stackelberg equilibrium solution concept describes optimal strategies to
commit to: Player 1 (termed the leader) publicly commits to a strategy and
Player 2 (termed the follower) plays a best response to this strategy (ties are
broken in favor of the leader). We study Stackelberg equilibria in finite
sequential games (or extensive-form games) and provide new exact algorithms,
approximate algorithms, and hardness results for several classes of these
sequential games
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
Equilibria in Sequential Allocation
Sequential allocation is a simple mechanism for sharing multiple indivisible
items. We study strategic behavior in sequential allocation. In particular, we
consider Nash dynamics, as well as the computation and Pareto optimality of
pure equilibria, and Stackelberg strategies. We first demonstrate that, even
for two agents, better responses can cycle. We then present a linear-time
algorithm that returns a profile (which we call the "bluff profile") that is in
pure Nash equilibrium. Interestingly, the outcome of the bluff profile is the
same as that of the truthful profile and the profile is in pure Nash
equilibrium for \emph{all} cardinal utilities consistent with the ordinal
preferences. We show that the outcome of the bluff profile is Pareto optimal
with respect to pairwise comparisons. In contrast, we show that an assignment
may not be Pareto optimal with respect to pairwise comparisons even if it is a
result of a preference profile that is in pure Nash equilibrium for all
utilities consistent with ordinal preferences. Finally, we present a dynamic
program to compute an optimal Stackelberg strategy for two agents, where the
second agent has a constant number of distinct values for the items
Stochastic Stackelberg games
In this paper, we consider a discrete-time stochastic Stackelberg game where
there is a defender (also called leader) who has to defend a target and an
attacker (also called follower). Both attacker and defender have conditionally
independent private types, conditioned on action and previous state, that
evolve as controlled Markov processes. The objective is to compute the
stochastic Stackelberg equilibrium of the game where defender commits to a
strategy. The attacker's strategy is the best response to the defender strategy
and defender's strategy is optimum given the attacker plays the best response.
In general, computing such equilibrium involves solving a fixed-point equation
for the whole game. In this paper, we present an algorithm that computes such
strategies by solving smaller fixed-point equations for each time . This
reduces the computational complexity of the problem from double exponential in
time to linear in time. Based on this algorithm, we compute stochastic
Stackelberg equilibrium of a security example.Comment: 31 pages, 6 figure
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