The payoff value for which each player in a game always selects the same strategy is called the

The payoff value for which each player in a game always selects the same strategy is called the "dominant strategy equilibrium."

Here are the steps to understand this concept:

1. In game theory, a player's strategy is any of the options they can choose in a setting where the outcome depends not only on their own actions but also on the actions of others.

2. A dominant strategy is a strategy that is the best choice for a player, no matter what strategies the other players choose.

3. If every player has a dominant strategy, and if each player plays their dominant strategy, then the outcome of the game is called the dominant strategy equilibrium.

4. In other words, a dominant strategy equilibrium is a situation in a game where every player chooses their dominant strategy, and no player can benefit from deviating from their strategy assuming the other players keep theirs unchanged.

5. Therefore, the payoff value for which each player in a game always selects the same strategy is called the dominant strategy equilibrium.