Financial Markets: Econ 326 Q1) Suppose you are trading in two assets, asset 1 a

Question

Financial Markets: Econ 326 Q1) Suppose you are trading in two assets, asset 1 and 2, with the asset returns, matrix: I 2l and prices 1 and 2, respectively. a. Find the two portfolios delivering returns (1,0) and (0,1) b. Find price of those portfolios. Could those prices arise at equilibrium? If yes, why? If no, why not? C. Consider a two-period economy with a complete set of financial securities with the same matrix of returns: Suppose that the risk-neutral probabilities for this economy are given by 1/3 and 2/3 for the first and second state, respectively and the discount factor is given by 2 Compute the prices of the assets. d. Suppose that the prices of the first and second asset, instead of being the prices computed in part (c), are given by 6 and 3, respectively. Show that there exists an arbitrage portfolio in this economy.

Explanation / Answer

In game theory, the Nash equilibrium, named after the late American mathematician John Forbes Nash Jr., is a solution concept of a non-cooperative game involving two or more players in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.[1] If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitutes a Nash equilibrium. The Nash equilibrium is one of the foundational concepts in game theory. The reality of the Nash equilibrium of a game can be tested using experimental economics methods[citation needed].

Stated simply, Alice and Bob are in Nash equilibrium if Alice is making the best decision she can, taking into account Bob's decision while Bob's decision remains unchanged, and Bob is making the best decision he can, taking into account Alice's decision while Alice's decision remains unchanged. Likewise, a group of players are in Nash equilibrium if each one is making the best decision possible, taking into account the decisions of the others in the game as long as the other parties' decisions remain unchanged.

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