# The LP formulation of finite zero-sum games with incomplete information

@article{Ponssard1980TheLF, title={The LP formulation of finite zero-sum games with incomplete information}, author={Jean Pierre Ponssard and Sylvain Sorin}, journal={International Journal of Game Theory}, year={1980}, volume={9}, pages={99-105} }

This paper gives the LP formulation for finite zero sum games with incomplete information using Bayesian mixed strategies. This formulation is then used to derive general properties for the value of such games, the well known concave-convex property but also the “piecewise bilinearity”. These properties may offer considerable help for computational purposes but also provide structural guidelines for the analysis of special classes of games with incomplete information.

## 48 Citations

### Repeated games with incomplete information and transportation problems

- EconomicsMath. Methods Oper. Res.
- 1999

The solutions for two person zero-sum repeated games with lack of information on one side and with payoffs of special “separable” form are reduced to the solutions for families of special transportation type problems with recursive structure.

### LP formulation of asymmetric zero-sum stochastic games

- Economics53rd IEEE Conference on Decision and Control
- 2014

This paper provides an efficient linear programming (LP) formulation of asymmetric two player zero-sum stochastic games with finite horizon that has its size to be linear with respect to the size of the state and thesize of the uninformed player, and hence greatly reduces the computational complexity.

### Formulation of Asymmetric Zero-Sum Stochastic Games

- Economics
- 2014

This paper provides an efficient linear programming (LP) formulation of asymmetric two player zero-sum stochastic games with finite horizon. In these stochastic games, only one player is informed of…

### Markov games with incomplete information

- Computer ScienceMath. Methods Oper. Res.
- 1997

Finite algorithms for computing optimal strategies for the informed and uninformed player are presented, based on linear programming results.

### Some results on zero-sum games with incomplete information: The dependent case

- Economics, Computer Science
- 1980

It turns out that many results obtained in the simpler independent case have their counterpart in the dependent one, proved in this paper for several previous results of the authors.

### Equilibrium Solutions of Two-Person Non-Zero-Sum Games in Extensive Form and the Corresponding Quadratic Programming Problems

- Mathematics, Economics
- 2004

This paper deals with two types of two-person non-zero-sum games in extensive form. We formulate quadratic programming problems whose decision variables correspond to behavioral strategies of players…

### Optimal strategies for the uninformed player

- Economics
- 1991

This paper provides a counterpart of the well-known recursive formula for finitely repeated zero-sum games with lack of information on one side from the point of view of the uninformed player.…

### Zero-sum Stochastic Games with Asymmetric Information

- Economics, Computer Science2019 IEEE 58th Conference on Decision and Control (CDC)
- 2019

It is shown that for this class of games, there exists a Nash equilibrium where the more informed player plays a common information belief based strategy and a dynamic programming approach is presented for computing this strategy.

### Upper and Lower Values in Zero-Sum Stochastic Games with Asymmetric Information

- EconomicsDyn. Games Appl.
- 2021

A general model for zero-sum stochastic games with asymmetric information is considered. In this model, each player’s information at each time can be divided into a common information part and a…

### Optimal Behavioral Strategies In 0-Sum Games with Almost Perfect Information

- EconomicsMath. Oper. Res.
- 1982

The general construction of the optimal strategies in a special class of zero sum games with incomplete information, those in which the players move sequentially, gives new insights on earlier results obtained in the context of sequential repeated games.

## References

SHOWING 1-3 OF 3 REFERENCES

### A note on the L-P formulation of zero-sum sequential games with incomplete information

- Economics, Mathematics
- 1975

Zero-sum games with incomplete information are formulated as linear programs in which the players' behavioral strategies appear as primal and dual variables. Known properties for these games may then…

### Zero-Sum Games with “Almost” Perfect Information

- Economics
- 1975

The present paper generalizes the concept of perfect information to games in which the players, while moving sequentially, remain uncertain about the actual payoff of the game because of an initial…

### The value of two-person zero-sum repeated games with lack of information on both sides

- Mathematics
- 1971

AbstractWe consider repeated two-person zero-sum games in which each player has only partial information about a chance move that takes place at the beginning of the game. Under some conditions on…