Consider the Following Two-Person Zero-Sum Game Is There an Optimal Pure Strategy for This Game? If

question 6

Essay

Consider the following two-person zero-sum game.Assume the two players have the same three strategy options.The payoff table below shows the gains for Player A. $$\begin{array}{l}\begin{array} { | c | c c c c | } &&\text { Player B }\\\\{ \text { Plaver } \mathrm { A } } & \text { Strategy } b _ { 1 } & \text { Strategy } b _ { 2 } & \text { Strategy } b _ { 3 } \\\hline \text { Strategy } a _ { 1 } & 3 & 2 & - 4 \\\text { Strategy } a _ { 2 } & - 1 & 0 & 2 \\\text { Strategy } a _ { 3 } & 4 & 5 & - 3 \\\hline\end{array}\end{array}$$ Is there an optimal pure strategy for this game? If so,what is it? If not,can the mixed-strategy probabilities be found algebraically? What is the value of the game?

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Definitions:

Cash Flow Matching

A form of immunization, matching cash flows from a bond portfolio with those of an obligation.

Immunization

A strategy in fixed income investing that aims to make a portfolio's duration and interest rate risk match its liability obligations.

Duration Matching

An investment strategy where the durations of assets and liabilities are aligned to reduce the risk of changes in interest rates affecting the net worth.

Duration

A measure of the sensitivity of the price of a bond or other debt instrument to changes in interest rates, frequently used to assess interest rate risk.