Prisoner Dilemma Game and Pareto Equilibrium

Condition for Pareto inferiority; z > x> 0 and that α < 0 and that:

 (NC, NC) = (αx, αx), (C, C) = (x, x), (NC, C) = (z, -z), (C, NC) = (z, -z) where NC implies not cooperative while C implies cooperative. This condition is not a Pareto optimal given that one player is cooperative while the other is not, the expected payoff is zero and given that 6 > 5 > 0, 0 < 1 the condition is Pareto-inferior equilibrium. The players cannot do better for themselves.

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      ii.   There is a general concept by economists that players would trade off any condition that is Pareto inferior whereas neoclassical theorists reason out that a number of trade conditions would not favor Pareto optimality. In the game, the players could do better for themselves if the organization can protect the independence of each player to enable each player reach an independent Pareto-optimal situation. In addition, the players may not have played together at any given point resulting to ignorance of new partners about each other.

VF = x(a), where xa > 0, xaa < 0 and also that x(0)> 1/ α, therefore by playing the game ten times the equilibrium will be given by VF = 10{x(a)}

For interaction with an informal player;

VI  = αx (a) which gives an equilibrium of 10{αx (a)} after ten interactions

The expected pay off is given by;

VFK, a > VIK -1, a = αωx (a) where VF is formal player and VI is an informal player.

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