This is clearly shown in the results of the triangle game, where responsibility ratings were proportional to players' deviations scores even for players that all satisfy the same criterion.
Consequently, when any player deviates from the new OP, the latter quantity changes and the deviation is then detected [18].
Hence, if any player deviates at any intermediate stage from (0,0) and then conforms to the strategy by playing (0,0), the stage payoff at the deviation will be lesser than the stage payoff if there was no deviation.
For a coalition of more than one player, a deviation is self-enforcing if (1) it is profitable for all its members and (2) if there is no further self-enforcing and improving deviation available to a proper sub-coalition of players.
He tracked the players' rhythmic deviations as they synchronized over 6 to 8 minutes.
For example, consider the Max condition in the triangle game, where each player's individual deviation from the correct answer must be less than 3. Compare two cases in which A and B are over the threshold: (a) players A and B both deviate by 3; (b) player A deviates by 3, player B deviates by 5. Is player A equally responsible in both cases?
In the Min condition, if player A deviates by 1 and player B deviates by 5, both are pivotal for the team's loss (changing either player to 0 would switch the loss to a win), but player A requires fewer changes (in deviation points) than player B to make him non-pivotal for the loss.
Secondly, in case there is a deviation by player k at stage τ+1, the discounted payoff is given by (v_{k}(widetilde {s})=) begin{aligned} frac{ 1-delta)}{(1-delta^{T})}&lefrac{ 1-delta{tau}delta^{ 1-delta^{alpha_{ 1-delta^{{-k}^)righT}
Unilateral deviation of player k1 from ψ = A F = { k 1, k 2 }, A D = ∅ to ψ = A F = { k 2 }, A D = { k 1 } increases its own payoff; therefore, the pure strategy profile (F,F) is not a Nash equilibrium point.
A strong equilibrium is defined as a strategic profile for which no subset of players has a joint deviation that strictly benefits all of them, while all other players (in the subset) are expected to maintain their equilibrium strategies.
