Non-cooperative game theory Flashcards
Classify the different types of game theory
Non-cooperative game theory - Self-interested agents
Cooperative game theory - Agents forming coalitions
Behavioral games - Discrepancy between reality and theory
Evolutional game theory - Agents in evolving populations
Explain what we mean by self-interested agents
Self interested agents have desires and beliefs and aims to maximize their expected utility.
a) How do we model utility?
b) Name a few properties of the preference orderings
c) Discuss the relation between utility and money
a) utility is modeled by a set of outcomes - Omega - and the chosen outcome -omega
b)
- Reflexivity - For all w in Omega we havethat w > w
- Transitivity - If w1>w2 and w2>w3 then w1>w3
- Comparability - For all w either w1>w2 or w2>w1
c) Utility is similar to money by the fact that in a capitalist society we often seek as “agents” to maximize the amount of money we receive from doing a task
What do we mean by strategic interaction?
What I do depend on what you do and what you do depend on what I do which we both should have taken into account in the first place.
- The environment is altered in simultaneous actions by agents
- Strategic interaction assumes that agent must act and that agents can see each other perform actions
The simplest strategic game is when two agents have two actions available: defect D and cooperate C
Then we have four possible outcomes: (C,C) (D,D) (C,D) and (D,C)
Name a few solution concepts for solving a 2x2 game on strategic form
Maximizing social welfare - gives most utility to all agents
Pareto efficiency - no improvement is possible without making
someone else worse of
Dominant strategy - Agents don’t care about what others do. No guarantee that there exists a solution.
Nash equilibrium - If there are two strategies for agent A and agent B and they chose the strategy that is best for them based on the other’s choice
a) Explain the Prisoner’s Dilemma
b) Why is it a dilemma?
c) Name a few important real-world PDs
a) Two people are in a prison and both receive a choice: betray your friend or don’t. If one betrays their friend and the other doesn’t, the betrayer goes free. If both betray they get a long sentence, but if none betray they get a short sentence.
b) The dilemma lies in the fact that rational agents would choose to betray their friend even though it ends up giving them a longer sentence than cooperating
c)
Overfishing the seas
Internet bandwidth capacity
Nuclear weapons treaties
How does repeating the PD game affect the outcome?
Infinite PDgame will lead to cooperation.
Finite iterations PDgame will lead to defect on last round, therefore they defect all the way, but can lead to cooperation if a threshold is set.
What do we mean by competitive games and zero-sum games?
Competitive games is an iteraction where it is said to be strictly
competitive among agent A and agent B when wz.ae for outcome w and w.
Zero sum games are formally described as we a where ui w is utility of agent c of outcome w
