A player adopting zero-determinant strategies is able to pin the expected payoff of the opponents or to enforce a linear relationship between his own payoff and the opponents’ payoff, in a unilateral way., In doing so, the player must ensure that the token stays within a (Euclidean) distance d d from (0, 0) (0, 0). In other words, if after a move the coordinates of the token are (p, q) (p, q), then p2 +q2 ≤ d2 p 2 + q 2 ≤ d 2 must hold. The game ends when a player is unable to make a move., After more than two decades, Gordon et al. [7] came with a set of functions for which complete fairness is possible for two-party computation in non-simultaneous channel model, even if one of the players is malicious., If the desired vector p RN exists for Example 1, then on one side p(N) > n/2 and on the other side ∈ p(N) < 2, showing that for n > 4 this game is not a weighted voting game. we could use the critical threshold value introduced in [4]. Before we define the critical threshold alue of a simple game, let us define the following, Additionally, by considering the asymptotic numbers of players, we propose two potential estimates for a ”fair” threshold: either 31.8% or 36.8% of the pie (share) for the responder. Ultimatum Game | | | Fairness | | | Multiplayer Games | | | Competition., Suppose two players are playing this game: each round they flip a coin. If it's Heads, P1 gets a point. If Tails, P2 gets a point. P1 needs X points to win, while P2 needs Y. What is the probability of P1 winning? Is the coin fair? It might be easier by imaging them flipping X + Y − 1 times..