# Game Theory 1 – Coursera

My first online course – Game Theory 1

https://www.coursera.org/learn/game-theory-1/

#### Why I took this course

I enjoy strategic games (poker, daily fantasy sports, board games, etc.), and I usually find examining optimal decisions and thought processes to be at least as fun as playing games themselves.

#### Review

4/5 – This course is well-organized and provides a helpful introduction to several game theory concepts. However, the professors focus more on theory and less on examples than I would prefer. I frequently had to search external sites to find additional examples on a given topic to improve my understanding. Also, at least one of the professors frequently spoke incorrectly during lectures, which added confusion. If this course was more expensive (it is free!), I would have been disappointed in the amount of time I had to spend on external resources. Between the introduction to game theory concepts and my supplemental research, I believe completing this course was a worthwhile exercise that helped improve my understanding of game theory.

#### Notes, Key Terms & Topics

- Nash Equilibrium
- A stable state of a system involving the interaction of different participants, in which no participant can gain by a unilateral change of strategy if the strategies of the others remain unchanged.
- In other words, no player gains an advantage by changing their decision when all other players cannot change their decision.

- Pareto Optimal
- An outcome of a game is Pareto optimal if there is no other outcome that makes every player at least as well off and at least one player strictly better off.
- That is, a Pareto Optimal outcome cannot be improved upon without hurting at least one player.

- Dominant Strategies
- A strictly dominant strategy is that strategy that always provides greater utility to a the player, no matter what the other playerâ€™s strategy is.
- A weakly dominant strategy is that strategy that provides at least the same utility for all the other playerâ€™s strategies, and strictly greater for some strategy.

- Prisoner’s Dilemma: Famous introductory game theory example:
- https://en.wikipedia.org/wiki/Prisoner%27s_dilemma
- The strictly dominant strategy for each player is to defect (turn in the other player), resulting in defect/defect as the Nash Equilibrium.
- However the Pareto Optima (and obvious best mutual outcome) would be for both players to cooperate with each other..

- Mixed-Strategy Nash Equilibrium
- At least one player playing a randomized strategy and no player being able to increase his or her expected payoff by playing an alternate strategy.
- For example, in soccer penalty kicks, a goalie should randomly guess left P% and the kicker should randomly kick right Q%.
- Sample Calculation:

- Minimax Strategy – A strategy of always minimizing the maximum possible loss which can result from a choice that a player makes
- Backward Induction
- Backward induction is the process of reasoning backwards in time, from the end of a problem or situation, to determine a sequence of optimal actions.
- It proceeds by first considering the last time a decision might be made and choosing what to do in any situation at that time.

- Bayesian Games – A Bayesian Nash equilibrium is defined as a strategy profile and beliefs specified for each player about the types of the other players that maximizes the expected payoff for each player given their beliefs about the other players’ types and given the strategies played by the other players.
- Shapley Value (Cooperative Game Theory)
- A manner of fairly distributing both gains and costs to several actors working in coalition.
- Calculated based on each player’s contribution when they played individually and the marginal value they add when combined with other players.

- Coalition Core – Basically, an outcome is in the core of a game if no subset of players could make themselves all better off by breaking away and playing the game among themselves.

#### Next Steps

- Read this book: The Art of Strategy by Dixit and Nalebuff
- Read this book: Modern Poker Theory by Michael Acevedo
- Complete the follow-up course: https://www.coursera.org/learn/game-theory-2/