### March 7, 2022

**Edwin Hamel**(Université libre de Bruxelles)

Parity games are well-known infinite two-player games played on finitely colored graphs. We define an extension of parity games, called counter games, where each player can at every move, increment or reset a finite number of counters.

We examine several types of winning conditions that are linked to the boundedness of the counters of the game, and to parity conditions. For every type of winning conditions examined, we give algorithmic complexity results, and results on the size of the memory needed to win. For example, we show that deciding whether Eve can force one of the counters to be bounded can be done in polynomial time, and that, if Eve wins, then Eve has a memoryless winning strategy.

The results in this talk are joint work with Emmanuel Filiot.