A leading authority in game theory and economic history, Professor Ben Polak of Yale University has influenced a generation of students and academics through his engaging lectures and insightful research.

On the Fundamentals of Game Theory

  1. On the nature of strategic situations: "Game theory is a way of analyzing strategic situations... any setting in which the outcomes that you might care about depend on actions of more than one person." [1]
  2. The essential components of a game: A game requires players, strategies, and payoffs. Until you know what people care about, you can't analyze the game. [2]
  3. On the limits of game theory: "Game Theory, me, professors at Yale, cannot tell you what your payoff should be. I can't tell you in a useful way what it is that your goals in life should be or whatever. That's not what Game Theory is about." [3]
  4. The two primary aims of game theory: "One aim of the course is to teach you some strategic considerations to take into account making your choices. A second aim is to predict how other people or organizations behave when they are in strategic settings." [4]
  5. The interconnectedness of strategic thinking: "We will see that these aims are closely related." [4]

On Rationality and Dominance

  1. The first rule of game theory: "Do not play a strictly dominated strategy." [3]
  2. The logic behind avoiding dominated strategies: "The reason I never want to play a strictly dominated strategy is, if instead I play the strategy that dominates it, whatever anyone else does I'm doing better than I would have done. Now that's a pretty convincing argument." [3]
  3. Definition of a strictly dominated strategy: "We say that my strategy Alpha strictly dominates my strategy Beta, if my payoff from Alpha is strictly greater than that from Beta, regardless of what others do." [3]
  4. Weak vs. a strong dominance: A strategy weakly dominates another if it does at least as well in all situations and strictly better in at least one. [2]
  5. The power of iterative deletion: "Since you shouldn't play a dominated strategy (and you know your opponent won't either), you can delete dominated strategies from the strategy set. But now that the game has changed, there may be new dominated strategies. These should be deleted again, and so on." [2]
  6. Rationality can lead to bad outcomes: Rational play by rational players can lead to Pareto inefficient outcomes, as seen in the classic Prisoners' Dilemma. [2][3]
  7. Real-world examples of the Prisoners' Dilemma: This can be seen in price competition in a duopoly, the use of common resources leading to overfishing, and other scenarios where individual incentives lead to collectively worse results. [2]

On Nash Equilibrium

  1. Introducing Nash Equilibrium: A Nash Equilibrium is a state where "each player is playing a best response to each other." [2]
  2. The "no regrets" principle: In a Nash Equilibrium, "no individual can do strictly better by deviating (holding others fixed) – no regrets." [2]
  3. The relationship between dominance and Nash Equilibrium: "No strictly dominated strategy can be part of a NE (by definition)." [2]
  4. Weakly dominated strategies and Nash Equilibrium: "However, weakly dominated strategies may be part of a NE." [2]
  5. Finding the best response: "Assuming your strategy set is continuous, the best response to an opponent's choice can be found by differentiating the payoff function with respect to your strategy, to find the strategy that maximises payoff." [2]
  6. The concept of "never-best response": "Some strategies are never the best responses, regardless of the opponent's choices. These never-best response (NBR) strategies are not rationalisable." [2]

On Different Types of Games and Strategies

  1. Sequential games and backward induction: In games where players move sequentially, one can often solve the game by reasoning backward from the end. [2]
  2. The power of backward induction: "Backward induction says to enter" in a market dominated by an incumbent who would rather not fight. [2]
  3. Mixed strategies in the real world: The concept of mixed strategies (randomizing one's actions) can be seen in sports like soccer (penalty kicks) and baseball, as well as in situations like paying taxes. [5]
  4. Evolutionary stability: This concept explores how strategies perform over time within a population, with applications to cooperation, mutation, and social conventions. [5]
  5. The Hawk-Dove game: A classic example in evolutionary game theory, this game models aggressive versus non-aggressive strategies in a competition for a resource. [2]
  6. Games of imperfect information: In these games, players do not know the entire history of moves, which adds a layer of complexity to strategic thinking. [2]
  7. Repeated games: The dynamic of a game changes significantly if it is played multiple times, as reputation and the possibility of future retaliation come into play. [2]
  8. Asymmetric information: This area of game theory deals with situations where one player knows more than another, leading to concepts like adverse selection and signaling. [4]

On Strategic Thinking and Decision Making

  1. The importance of putting yourself in others' shoes: A fundamental lesson in game theory is to think about what the other players will do. [5]
  2. The "2/3 game" and levels of rationality: "You have to estimate the group's rationality, and the group's view of the group's rationality, etc." [2]
  3. The duel as a game of timing: "In this game there's no question about what you're going to do... but the critical question is when you would do it." [6]
  4. Patience as a virtue in strategic situations: In the context of a duel, "Even if you are playing an irrational opponent, you shouldn't shoot before d* because it is a dominated strategy. Patience is a virtue!" [2]
  5. The importance of commitment and credibility: These concepts are crucial in strategic interactions, as making your threats or promises believable can alter the outcome of a game. [4]
  6. The value of a "dominance argument": "If I think P then I should do X. and if I think not P then I should do X therefore I should do X. All right dominance arguments pretty straightforward. But people get them wrong." [6]

On the Broader Applications and Implications of Game Theory

  1. Game theory in economics: It is used to model competition between firms (e.g., Apple vs. Google), as well as cooperation within teams. [6]
  2. Game theory in politics: The median-voter theorem is an application of iterative deletion of dominated strategies. [5]
  3. Game theory in biology: It is used to understand evolutionary dynamics and animal behavior. [3]
  4. Game theory in law: "Game Theory is very important in law these days. So for those of you--for the half of you--that are going to end up in law school, this is pretty good training." [3]
  5. Game theory in sports: Concepts from game theory are applied to analyze strategies in various sports. [3]
  6. Modeling cooperation: "It isn't only competition that we can model we can also model settings of cooperation." [6]
  7. The challenge of "herding cats": "Game theory is also the way you analyze how to herd cats." [6]
  8. On his Open Yale Course: "It's not the full Yale experience, unfortunately, but it's something.” [7]

Learnings from his Research and Academic Work

  1. Expertise in diverse fields: Professor Polak is an expert in decision theory, game theory, and economic history. [8]
  2. Exploring richer economic models: "His work explores economic agents whose goals are richer than those captured in traditional models." [8]
  3. Foundational work on common knowledge: His research in game theory includes foundational theoretical work on the concept of common knowledge. [8]
  4. Contributions to repeated games with asymmetric information: He has made recent contributions to the theory of how games unfold when played multiple times with unequal information among players. [8]
  5. Research on economic inequality: His other research interests include economic inequality and individuals' responses to uncertainty. [8]
  6. Empirical work on the Industrial Revolution: He has been engaged in an ambitious empirical project on industrial organization during the Industrial Revolution in England. [8]
  7. Investment incentives in trading: His research has characterized surplus-maximizing trading mechanisms, considering the trade-off between providing investment incentives and ensuring voluntary participation. [9]
  8. Dynamic markets: He has developed models of dynamic markets with randomly arriving buyers and sellers. [9]
  9. Judgment aggregation: He has co-edited a special symposium and written on the aggregation of individual judgments into a collective decision. [10]
  10. On the complexity of real-world problems: When analyzing a strategic problem, "it's not obvious it's not at all obvious... we want the right answer not the politicians answer so we're going have to do better than that." [1]

Sources:

Learn more:

  1. 4/14/12 Ben Polak - Game Theory and Staying Alive - YouTube
  2. Game Theory – Yale (Econ 159) - Reasonable Deviations
  3. ECON 159 - Lecture 1 - Introduction: Five First Lessons | Open Yale Courses
  4. Game Theory | Open Yale Courses
  5. Game Theory with Ben Polak - YouTube
  6. Game Theory - YouTube
  7. Ben Polak - Wikipedia
  8. Benjamin Polak | Yale School of Management
  9. Ben Polak's research works | Yale University and other places - ResearchGate
  10. BENJAMIN POLAK - Yale Department of Economics