## Monday, October 12, 2015

### Game Theory (3.5 out of 5 stars)

Note: This post represents the synthesis of the thoughts, procedures and experiences of others as represented in the  articles read in advance (see previous posts) and the discussion among the students and instructor during the Advanced Analytic Techniques class at Mercyhurst University in October 2015 regarding Game Theory as an Analytic Technique specifically. This technique was evaluated based on its overall validity, simplicity, flexibility and its ability to effectively use unstructured data.

Description:
Game theory is a method of analysis that mathematically models conflict and cooperation between rational actors. Game theory can be understood intuitively by assessing how actors behave in situations in which they have a vested interest. Quality game theory models incorporate real-world constraints such as limited time, levels of uncertainty, and incomplete information. Games are solved by looking ahead and anticipating actions of the opposing actor, while the opposing actor is simultaneously engaging in similar activities. It is expected that actors will make decisions in their own self-interest, but this has been refuted when actors cooperate or act in the best interest of the group.

Strengths:
• Gives quantitative results to analysis
• Types of game theory studies do not require knowledgeable experimenters
• Represents costs and benefits for all actors
• Can account for human behaviors to a degree
• Various types of game theory exist allowing different applications to a diverse range of problems
• Useful in various simulations where assigning a numeric value is usually required

Weaknesses:
• Assumes actors are rational thinkers
• Human mind is frequently social, not rational
• Applying this method to intangible problems is very difficult
• A complicated technique to learn and implement correctly
• Bundles human nature
• Can be susceptible to biases
• Highly favors quantitative inputs
• Requires 100% accurate information
• Non-cooperative and cooperative games will yield different results
• The questions must be asked in a specific way

How-To: For the scenario described in the personal application, analyst must construct a payoff matrix to answer the questions provided by the exercise.

In a payoff scenario,

1. Determine the problem and the players involved in the scenario.
2. Determine the strategies of each player.
3. Determine the payoff values for the payoff matrix.
4. Determine the dominant strategies

Personal Application of Technique:
###### Exercise 1 (Training and payment system, By Kim Swales)
Two players: The employee (Raquel) and the employer (Vera). Raquel has to choose whether to pursue training that costs £1, 000 to herself or not.  Vera has to decide whether  to pay a fixed wage of £10, 000 to Raquel or share the revenues of the enterprise 50:50 with Raquel. The output is positively affected by both training and revenue sharing. Indeed, with no training and a fixed wage total output is £20, 000, while if either training or profit sharing is implemented the output rises to £22, 000. If both training and revenue sharing are implemented the output is £25,  000.

1. Construct the payoff matrix
2. Is there any equilibrium in dominant strategies?
3. Can you find the solution of the game with Iterated Elimination of Dominated Strategies?
4. Is there any Nash equilibrium?
Solution
This game has the following characteristics:
• Players: Raquel and Vera
• Strategies:
• Raquel’s:  pursue training (costly to herself: £1, 000), or not
• Vera’s:  give revenue sharing (50:50), or fixed wage   (£10,000)
Payoffs: depend on total output and the way it is split. Output depends positively upon two factors: whether Raquel has training and if Vera adopts profit  sharing.
• Fixed wages + no training: output = 20,000
• Add either training or revenue share: output =  22,000
• Both training and revenue share: output = 25,000
We can then build the payoff matrix: with unit of account:  £/000
2. No, there is no equilibrium in dominant strategies because Raquel has no dominant strategy.  She prefers to train only if Vera  gives revenue sharing, while prefers not to  train with a fixed  wage.
3.  Yes. Fixed wage is a dominated strategy for Vera. Assuming that players are rational and that this information is common knowledge, Raquel knows that Vera will never choose a fixed wage. Then she will choose to train because No training is a dominated strategy after the elimination of Vera’s dominated strategy.
4. Yes. Every equilibrium identified by Iterated Elimination of Dominated Strategies is a Nash equilibrium.