satisfies this condition, the new state is called a "Pareto improvement". When no Pareto improvements are possible, the state is a "Pareto optimum". In other words, Pareto efficiency is when it is impossible to make one party better off without making another party worse off. This state indicates that resources can no longer be allocated in a way that makes one party better off without harming other parties. In a state of Pareto Efficiency, resources are allocated in the most efficient way possible. Pareto efficiency is mathematically represented when there is no other strategy profile s’ such that ui (s’) ≥ ui (s) for every player i and uj (s’) > uj (s) for some player j. In this equation s represents the strategy profile, u represents the utility or benefit, and j represents the player. Efficiency is an important criterion for judging behavior in a game. In a notable and often analyzed game known as Prisoner’s Dilemma, depicted below as a normal form game, this concept of efficiency can be observed, in that the strategy profile (Cooperate, Cooperate) is more efficient than (Defect, Defect). Using the definition listed above, u(Ci) ≥ u(Di) for i ∈ {1, 2}, thus yielding this strategy as a Pareto efficient strategy. In other words, both players receive an increase in payoff by selecting Cooperate over Defect. In zero-sum games, every outcome is Pareto-efficient. A special case of a state is an allocation of resources. The formal presentation of the concept in an economy is the following: Consider an economy with agents and goods. Then an allocation , where for all i, is Pareto-optimal if there is no other feasible allocation where, for utility function for each agent , for all with for some . Here, in this simple economy, "feasibility" refers to an allocation where the total amount of each good that is allocated sums to no more than the total amount of the good in the economy. In a more complex economy with production, an allocation would consist both of consumption vectors and production vectors, and feasibility would require that the total amount of each consumed good is no greater than the initial endowment plus the amount produced. Under the assumptions of the first welfare theorem, a competitive market leads to a Pareto-efficient outcome. This result was first demonstrated mathematically by economists Kenneth Arrow and Gérard Debreu. However, the result only holds under