# Computing the optimal strategy to commit to

@inproceedings{Conitzer2006ComputingTO, title={Computing the optimal strategy to commit to}, author={Vincent Conitzer and Tuomas Sandholm}, booktitle={ACM Conference on Economics and Computation}, year={2006} }

In multiagent systems, strategic settings are often analyzed under the assumption that the players choose their strategies simultaneously. However, this model is not always realistic. In many settings, one player is able to commit to a strategy before the other player makes a decision. Such models are synonymously referred to as leadership, commitment, or Stackelberg models, and optimal play in such models is often significantly different from optimal play in the model where strategies are…

## 488 Citations

### Commitment to Correlated Strategies

- EconomicsAAAI
- 2011

It is shown that these linear programs can be naturally merged into a single linear program, which can be interpreted as a formulation for the optimal correlated strategy to commit to, giving an easy proof of a result by von Stengel and Zamir that the leader's utility is at least the utility she gets in any correlated equilibrium of the simultaneous-move game.

### Optimal Machine Strategies to Commit to in Two-Person Repeated Games

- Computer ScienceAAAI
- 2015

This paper gives a concise linear program to compute the optimal leader’s strategy and gives two efficient implementations of the linear program: one via enumeration of a convex hull and the other via randomization.

### Computing the Strategy to Commit to in Polymatrix Games

- EconomicsAAAI
- 2018

This paper studies the computational complexity of finding or approximating an optimistic or pessimistic leader-follower equilibrium in specific classes of succinct games---polymatrix like---which are equivalent to 2-player Bayesian games with uncertainty over the follower, with interdependent or independent types.

### Computational Aspects of Stackelberg Games

- Computer Science
- 2013

This work focuses on Stackelberg security games, and offers a simple model of interdependencies between nodes in a network based on probabilistic failure cascades, extending the well-known independent cascade model of the spread of infectious diseases or ideas.

### Computing the optimal distributionally-robust strategy to commit to

- EconomicsArXiv
- 2022

The Stackelberg game model, where a leader commits to a strategy and the follower best responds, has found widespread application, particularly to security problems. In the security setting, the goal…

### Playing games for security: an efficient exact algorithm for solving Bayesian Stackelberg games

- Computer ScienceAAMAS
- 2008

This paper considers Bayesian Stackelberg games, in which the leader is uncertain about the types of adversary it may face, and presents an efficient exact algorithm for finding the optimal strategy for the leader to commit to in these games.

### Learning and Approximating the Optimal Strategy to Commit To

- Computer ScienceSAGT
- 2009

This work considers the computation of optimal Stackelberg strategies in general two-player Bayesian games, given that all the payoffs and the prior distribution over types are known.

### Team-Maxmin Equilibrium: Efficiency Bounds and Algorithms

- EconomicsAAAI
- 2017

Borders of (in)efficiency of the Team-maxmin equilibrium w.r.t. the NashEquilibrium when the team members can play correlated strategies are investigated, as well as a number of algorithms to find and/or approximate an equilibrium.

### Disarmament Games

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- 2017

This paper studies disarmament for two-player normal-form games, and shows that deciding whether an outcome can be obtained with disarmament is NP-complete (even for a fixed number of rounds), if only pure strategies can be removed.

## References

SHOWING 1-10 OF 29 REFERENCES

### Leadership with commitment to mixed strategies

- Economics
- 2004

A basic model of commitment is to convert a game in strategic form into a “leadership game” where one player commits to a strategy to which the other player chooses a best response, with payoffs as…

### Complexity Results about Nash Equilibria

- EconomicsIJCAI
- 2003

A single reduction demonstrates NP- hardness of determining whether Nash equilibria with certain natural properties exist, and demonstrates the NP-hardness of counting NashEquilibria (or connected sets of Nash Equilibria).

### Computing Nash Equilibria of Action-Graph Games

- EconomicsUAI
- 2004

This talk will survey two graphical models for compactly representing single-shot, finite-action games in which a large number of agents contend for scarce resources, and presents algorithms for computing both symmetric and arbitrary equilibria of AGGs.

### Efficient Computation of Equilibria for Extensive Two-Person Games

- Economics
- 1996

Abstract The Nash equilibria of a two-person, non-zero-sum game are the solutions of a certain linear complementarity problem (LCP). In order to use this for solving a game in extensive form, the…

### Mixed-Integer Programming Methods for Finding Nash Equilibria

- EconomicsAAAI
- 2005

The first mixed integer program (MIP) formulations for finding Nash equilibria in games (specifically, two-player normal form games) are presented and different design dimensions of search algorithms that are based on those formulations are studied.

### Complexity of (iterated) dominance

- EconomicsEC '05
- 2005

This work studies various computational aspects of solving games using dominance and iterated dominance, and shows that determining whether there is some path that eliminates a given strategy is NP-complete with iterated weak dominance and that iterated strict dominance becomes path-dependent when there is a limit on the support size of the dominating strategies.

### A polynomial-time nash equilibrium algorithm for repeated games

- EconomicsEC '03
- 2003

This approach draws on the "folk theorem" from game theory and shows how finite-state equilibrium strategies can be found efficiently and expressed succinctly in a polynomial-time algorithm.

### A Generalized Strategy Eliminability Criterion and Computational Methods for Applying It

- EconomicsAAAI
- 2005

It is shown that checking whether a strategy is eliminable according to this criterion is coNP-complete (both when all the sets are as large as possible and when the dominator sets each have size 1), and how this alternative definition can be translated into a mixed integer program of polynomial size.