Exercise 4 Consider the accompanying zerosum payoff table CI

Exercise 4 Consider the accompanying zero-sum payoff table CI -1 0 Firm Z C2 -2 CS RI Firm R2 R3 0 Does either player have a dominant strategy? Does either have a dominated strategy? Once you have eliminated one dominated strategy, solve for the equilibrium by iteratively eliminating dominated strategies. What strategies will the players use? What business case could the payoff matrix describe?

Solution

Yes, using the Maximin and Minimax procedure R₂ is the dominant strategy for firm Y and C₁ is the dominant strategy for fimrm Z.

Col.Max:0 4 4

Row Min:-2 0 -2

In utilizing every strategy, firm Y moves carefully and accept that whatever procedure it utilizes, its adversary will dependably receive that counter-technique which will give Y the base result. In this manner each time Y embraces a method, its benefit is lessened to the minimum by Z\'s counter ­strategy.

In this way, Y will pick that strategy which gives it the minimum out of the three most extreme pay-offs in each column.

Firm Z is additionally wary about the counter-strategy of its adversary Y. Z realizes that whatever move it will make in embracing a specific technique, Y will balance it by receiving a counter-methodology, along these lines leaving Z with a more awful result. Z\'s more awful result implies that Y gets vast benefit and Z is left with a next to no lingering.

The most extreme result from every methodology is in this way 0, 4 and 4 appeared in \"Col. Max\" (section maxima) . The best of these compensation offs from Z\'s perspective is the minimum of the section maxima, 0. It is known as the minimax, and the technique utilized by the minimiser is the minimax methodology. This is Z\'s
dominant strategy.

The saddle point is the balance point. In the result network of Table given, Y\'s result from its maximin procedure R₂ precisely measures up to Z\'s result from its minimax system C₁ (0=0). At the point when the minimax and the maximin in a result network are equivalent, it is an entirely a determined game. Both the players (firms) are ensured a typical measure of win (benefit). They can\'t win more on the grounds that there is a seat point in the result framework which happens both in the \"Column Min\", and \"Col. Max\". It is the harmony point 0, regular to both Y and Z.

Hence a constant-sum-two-person game is entirely decided just in the event that it has a seat point touched base at with unadulterated methodology. The determinate arrangement of the duopoly circumstance talked about above is completely in view of unadulterated procedure whereby each firm reasons out which of the few conceivable approaches are the most ideal to it.

In a remarkably decided diversion with unadulterated technique, there is no requirement for perceiving shared inter­dependence with respect to the duopolists. The minimax technique took after by Z can\'t be enhanced by the maximin methodology embraced by Y, if the result framework has a seat point. Along these lines, the duopoly circumstance turns out to be entirely determinate. The minimax technique is a contrasting option to benefit expansion. Through this procedure a firm limits the odds of the most extreme misfortune.