Game Theory

Descending Bid

prices fall as the auction advances. A Dutch auction follows this procedure with a price clock that decreases as the object is auctioned.

Playing Prisoner's Dilemma

1) Is there a dominant strategy? 2) Does any other player have a strictly DOMINATED strategy?

Strategies

A comprehensive plan of action for every contingency in a game. -action = a move at a specific stage of the game -Strategy = an action for every possible decision a player can face. The player considers other decisions and what will happen down the road.

Subgame perfect equilibrium

A decision node and following nodes in a sequential game in a game tree.

Revenue Equivalence

All common auction formats yield the same expected revenue (in theory) In the real world, risk averse people are more aggressive in first price or dutch auctions. inexperienced people overbid in second price, sealed bid auctions.

Simultaneous Games

Anticipating rival's moves

Open Auction (sequential)

Ascending price auction, where the highest bidder gets the item.

outcry auction

Bidders call out prices

Prisoner's Dilemma and Examples

Both Players have a dominant strategy, but the equilibrium has a lower payoff for each player. -Pricing by firms -divorce -nuclear weapons building -State governments and tax breaks (attract businesses)

Interactive Decision Theory

Choosing options while keeping other options in mind to obtain a given result -Never assume an opponent's behavior is fixed. For example, giving kids helmets in football does not necessarily mean less injuries because kids now have a greater incentive to act recklessly while wearing helmets. -airlines and child seats, too, because higher plane ticket prices = more road travel = more dangerous -Each change changes everything else. Always think about other's strategies than your own when playing game

Games Economists Play

Collusion, Standards Setting, Market Entry, Business Tax Breaks

Games of Coordination

Complements + technology adoption -2 firms, and each have preferred technology and the equilibrium is not a sure prediction. Must commit first to win.

Games of Assurance

Depends on trust between players. -joint research ventures, both need to invest for profits.

Games of chicken

Entry into small markets -airlines going into a small, local airport.

Sealed Bid first and second price

First: winner pays the highest bid. The best strategy here is to bid below true value. If you bid your true value, there is no surplus. You want to Shade bids. Second: buyer submitting the highest bid pays the second highest amount. The best way to bid in this auction is to bid your true valuation, strategically equivalent to an English auction.

History of Game theory

G.T. was a tool set for the government in defense/relations globally to prevent nuclear war. It was also useful for mathematics.

Social Behavior in Pigs

Getting food versus pressing the pedal, and the small pig's incentives.

Games We play

Group assignments, Prisoner's Dilemma, Free Riding, Mixed Strategies, Chicken, sequential games, Simultaneous games

Dominance Strategy

If it outperforms all other strategies, no matter what other players do. Games where both players have a dominant strategy are easy to solve. -Strictly Dominant = Strictly dominates all other strategies -Weakly Dominant = Sometimes other strategies earn just as much. (In reply to player 2's X, player 1's A and C move earn 10 utils.... This is weakly dominant strategy)

Sequential Games in a TIE

If payoffs are the same for 2 players while reasoning back nodes in the tree, draw the tree that picks both scenarios.

Best Reply

If this reply does at least as good as your opponent.

rationality and common knowledge with strategies

Knowing the other player is trying to play dominant strategy and knowing the best response to their dominant strategy.

Sequential Games

Looking forward and reasoning back

Changing the Rules

Majority Rule Votes: There is no majority in a three way race. Setting the rules gets you the outcome you desire, and when rules are flexible, manipulate them to your advantage

Payoffs

Numbers associated with each outcome. These numbers reflect the interests of the players. These numbers are sometimes ORDINAL (A better than B) and sometimes CARDINAL (A = 2B). -Utility has to do with personal preferences and payoffs (fairness and money) -Payoffs DRIVE and MOTIVATE players

Participants

Players are everyone who impacts your earnings, or whose actions you care about. -For example, government, employees, customers, investors and suppliers.

Multiple Equilibria

Predictability only if both prefer one equilibrium to another, known as "parete dominates". -Some refinements include picking the safer option given some differing sentiment. -Focal points and finding focal points of focal points

Assumptions

Rationality + Common Knowledge -Rationality = Players aim to maximize their profits, players are perfect calculators, and players know their payoffs and never make mistakes. -Common Knowledge = Each player KNOWS the rules of the game and is aware of other's knowledge of whats going on (Both knowledge and mutual knowledge that they know that I know that they know, etc. etc.), and rules of the game (players, payoffs, strategies, timing, and information)

Sequential Games

Simultaneous is not knowing information of other players' moves, and sequential is knowing the information and reacting accordingly. -To solve sequential games, first start at the END. Trim the tree to present decision. Eliminate non credible choices. -Pick the last move and pick the higher outcome/payoff for that player's decision. Then match/play that outcome combination against player before them.

Rules of the Game

The Participants, Rules, and Assumptions -Participants, Strategies and Payoffs

Equilibrium

The likely outcome of a game when rational, strategic agents interact. Each player plays their best strategy when given choices of other players, and no player has incentive to change decision unilaterally. -The equilibrium may not always be efficient and players may be forced to accept unfavorable outcomes.

Game Theory Definition

The study of rational behavior of individuals in interdependent situations. Game theory develops a framework for thinking about strategic interactions because most games and winning and losing in real life is not set in stone.

Timing of Moves

Whether moves are simultaneous or sequential has to do with INFORMATION. This information distinction is simply who knows what and when. -For example, 2 companies making a pricing decision will not know what the other company's move is and has to best guess (Simultaneous) or react to the other company's first move if information is leaked (Sequential)

dutch auction

a descending auction with a price clock that decreases in value.

silent auction

auctioneer calls out the prices

Japanese auction

bidders hold down a button until they no longer want to bid that high.

Sealed auction (simultaneous)

bidding a price privately and paying that price if you win. Writing it down on a sheet of paper, for example.

Ascending Bid

higher and higher bids throughout the auction, as long as someone bids higher than the previous bidder.

Private value (source of uncertainty)

i know the worth of the item and do not care about other's value. Bidders differ in their value for the object. Dinner would be an example. -do not bid more than your true value or less than your costs.

Auctions

marketing institution with rules governing resource allocation on basis of bids and participation. some examples of things auctioned include the right to broadcast, initial public offerings, and providing electric power.

Common value (source of uncertainty)

the item has a single, but unknown value. People have beliefs about the value of object but willing to change. an unproven oil field is a good example of this. -winner can be wrong