# Zero-sum repeated games: Counterexamples to the existence of the asymptotic value and the conjecture operatornamemaxmin=operatornamelimvn

arXiv: https://arxiv.org/abs/1305.4778 · HTML: https://mlsanity.com/paper/1305.4778/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2013.

## Built on by (most cited first, 2 of 2)

- [Bellman Optimality of Average-Reward Robust Markov Decision Processes with a Constant Gain](https://mlsanity.com/paper/2509.14203/) (2025)
- [Time-Dependent Blackwell Approachability and Application to Absorbing Games](https://mlsanity.com/paper/2303.04956/) (2023)

## Abstract (arXiv)

Mertens [In Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986) (1987) 1528-1577 Amer. Math. Soc.] proposed two general conjectures about repeated games: the first one is that, in any two-person zero-sum repeated game, the asymptotic value exists, and the second one is that, when Player 1 is more informed than Player 2, in the long run Player 1 is able to guarantee the asymptotic value. We disprove these two long-standing conjectures by providing an example of a zero-sum repeated game with public signals and perfect observation of the actions, where the value of the λ-discounted game does not converge when λ goes to 0. The aforementioned example involves seven states, two actions and two signals for each player. Remarkably, players observe the payoffs, and play in turn.