Question

Present an example of game theory using a matrix format.. Show how the solution is determined, and cite your source

Answer 1

Example:

The labor contract between a company and the union will terminate in

the near future. A new contract must be negotiated. After a

consideration of past experience, the group (Co) agrees that the

feasible strategies for the company to follow are:

C1 = all out attack; hard aggressive bargaining

C2 = a reasoning, logical approach

C3 = a legalistic strategy

C4 = an agreeable conciliatory approach

Assume that the union is considering one of the following set of

approaches:

U1 = all out attack; hard aggressive bargaining

U2 = a reasoning, logical approach

U3 = a legalistic strategy

U4 = an agreeable conciliatory approach

Interpretation of above table or game matrix

If Co. adopts C1 and Union adopts U1, the final contract involves a P2.0 increase in wages (hence, a -P2.0 loss to the company).

From the above table, it is clear that if the Company decides to adopt C3, Union will adopt U1.

If the Union decides to adopt U3, the company will adopt C2.

U1 dominates U4. U4 can therefore be removed from the gamematrix.

After removing U4, we see that C2 dominates C1. C1 can likewise be removed from the table.

We are now left with a 3x3 game matrix. This time, we see that U1 dominates both U2 and U3. U2 and U3 can also be removed from the table which leaves us with a 1x3 row vector.

Finally, C3 dominates C2 and C4.

This leaves us with a single value of 1.2 which corresponds to the value under C3 and U1 in the original game matrix.

As we already know, C3 and U1 represents the pure strategy solution to this game theory problem.