Game Theory in Business: Strategies, Insights, and Applications

Game theory: Examination of strategically intertwined behavior. Strategic interdependence is a way of illustrating scenarios where my actions impact your results, and conversely, your actions influence my outcomes.

It provides us with a versatile framework that encompasses not only competitive situations but also collaborative endeavors where both parties seek to succeed. It further extends to scenarios that lie between

Let's Start with the Basics

Chapter One delves into the world of simultaneous move games. These are scenarios where players must formulate their strategies independently, without the luxury of observing their opponents' choices. Think of situations like

• Penalty kicks in soccer
• Interrogations in isolated prison cells
• Deciding whether to halt at a stoplight.

We'll explore key concepts and strategies, including strict dominance, iterated elimination of strictly dominated strategies, pure strategy Nash equilibrium, best responses, mixed strategy Nash equilibrium, and weak dominance.

Extensive Forms of Games

We now enter a realm of turn-based actions. Consider scenarios like war and invasion plans and police searches.

In this chapter, we'll explore concepts such as backward induction, subgame perfect equilibrium, credible threats, tying hands, commitment problems, and forward induction.

Advanced Strategic Form Games

An extension of what we covered in Chapter One, but with a broader perspective. This allows us to tackle critical questions, like why a soccer striker may kick left more frequently as their accuracy on the left side improves. We'll also dive into topics like comparative statics, which is at the core of game theory, knife-edge equilibria, and symmetric zeroes.

The Prisoner's Dilemma and Strict Dominance

Let's dive into the classic scenario known as the Prisoner's Dilemma, where two suspects find themselves in a perplexing situation:

Situation: Two suspects have been arrested, suspected of robbing a store. However, the police only have evidence to charge them with trespassing. To build a case for the more severe crime, the police need one of the suspects to confess.

To encourage a confession, the police introduce the prisoners to a dilemma:

The Dilemma:

• If neither suspect confesses, both are charged with trespassing, resulting in a one-month jail sentence for each.
• If one confesses while the other remains silent, the confessor goes free, and the quiet one faces a twenty-month jail term.
• If both confess, they are both charged with robbery, incurring an five-month jail sentence.

The question at hand: Assuming the suspects only care about their own well-being, should they confess to the police?

The Payoff Matrix:

• Player A (Orange) and Player B (Blue) have two strategies: confess or keep quiet.
• Payoffs:Both keeping quiet: 1 months for each. One confesses, one keeps quiet: 0 months for the confessor, 20 months for the quiet one.
• Both confess: 5 months for each.

Solving the Dilemma:

• If Player A knows Player B will keep quiet, Player A is better off confessing (0 < 1).
• If Player A knows Player B will confess, Player A is still better off confessing (5 < 20).
• Player A's confess strategy strictly dominates keep quiet.

Key Insight: Rational players never choose strictly dominated strategies; they always aim for a better outcome.

• Player A will confess.
• Now, consider Player B:If Player B knows Player A keeps quiet, Player B is better off confessing (0 < 1).If Player B knows Player A confesses, Player B is still better off confessing ( 5 < 20).

The Result: Both players will confess, resulting in 5 months for each, even though collectively, both keeping quiet is a better outcome (1 and 1). However, the individual interest in confessing prevails.

Real World example from Pharma-world on Prisoner's dilemma

In the early 2000s, Roche faced a competitive scenario with its cancer drug Avastin and ImClone Systems' Erbitux, both targeting colorectal cancer.

Application of Game Theory:

1. Pricing Strategies: Roche and ImClone had to carefully price their drugs, considering each other's moves to gain market share.
2. Clinical Trial Timing: Both companies strategically timed clinical trial result releases to gain a competitive edge.
3. Market Access: They predicted how pricing strategies would impact patient access through insurance and healthcare providers.
4. Negotiations: Game theory influenced negotiations with insurers and healthcare providers, where pricing played a significant role.

In this example, game theory helped Roche and ImClone navigate a competitive market for cancer drugs, impacting patients and profitability. Specific cases may change over time; for current examples, refer to recent news or industry reports.

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