List of games in Chapter 8 Dominance

Using Comlabgames

 

Game title

(right click on the game to download it)

Short description of the experiment

Game 8.1: Prisonerís dilemma

Lacking evidence that might solve a heinous crime and facing public outcry, the police force in a country with a poor civil rights record randomly arrests two strangers, and charges them with committing the crime together. They are questioned separately, and given the opportunity to plea bargain. If neither of the arrested parties, or prisoners, confess to the heinous crime both are detained for a stiffer interrogation, but ultimately allowed to go free after a human rights organization has brought attention to their plight. If one of them coop confesses that they pared up and committed the crime together, he is forgiven for the remorse he has shown and the other prisoner is executed in public. If both parties confess a long goal sentence meted out to both prisoners.

Game 8.2: Team production with more generous bonus designed in free form

 

A firm sells output that is jointly produced by a design team and a manufacturing team. The quality of the output determines the price for which it can be sold. To keep matters simple, we assume that for each extra unit of effort undertaken by either team, up to 10 units, sales rise by $1.5million per unit. Any input beyond 10 within either team is wasted effort, producing no marginal increase in sales. It costs $1million per unit of effort in either team, in terms of lost sleep, hiring new staff, and buying new equipment (plant) and materials. Effort is not observed by the management. To compensate design and manufacturing, management institutes a profit sharing plan, whereby design and manufacturing each get one-third of the sales as compensation. Furthermore if the firm reaches its sales target of $30 million, it will also distribute a bonus of $100,000 dollars to both teams.

 

Game 8.3: Team production with more generous bonus designed with the strategic form

Game 8.4: Team production with less generous bonus designed in free form

To compensate design and manufacturing, the firm pays each team compensation of $10 million plus a $50,000 bonus each if both teams reach the profit target of $30m. Otherwise they get nothing.

Game 8.5: Team production with less generous bonus designed with the strategic form

Game 8.6: Essay

Games with dominated strategies do not necessarily have dominant strategies.

The strategy of submitting gibberish is dominated by submitting an original contribution.

Game 8.7: Market groceries

Supermarkets compete with local grocery stores for business. We model the

nature of their competition as a choice over three attributes shoppers value,

the prices of their products, the range of products, the length of the

checkout, the air-conditioning system within the store, ease of close

parking and other customer services, and the hours of operations each

day and proximity to demanders. Supermarkets typically occupy a

very different location in the attribute spectrum to a corner store franchise, and on

a much larger scale, so this is reflected in the bimatrix payoff entries.

Game 8.8: Duopoly, price competition

In a Bertrand pricing game between two firms, both firms set the price of their product and fulfill all orders on demand. We denote by p1 the price set by the first firm, and p the price set by the second firm. The vector (p1,p) are the choice variables in this simultaneous move game. For experimental purposes it is useful to imagine that prices charged from a discrete set (perhaps because the units prices are denominated in whole dollars or cents) a discrete version of the pricing game.

Game 8.9: Duopoly, quantity competition

An alternative to competing on price is to compete on quantity, by choosing production levels and letting the market determine the price that keeps inventory levels roughly constant.

Game 8.10: First price sealed bid auction in strategic form

We assume that one bidder values the item at $4 million, and the other at $2 million. To calculate the expected payoffs when both players make the same bid, we assume each bidder stands an equal chance of winning the auction. Accordingly consider the top left matrix entries, which give the expected payout to both players ($0.5 million, $1.5 million) if both players bid $1 million. Since there is a 50 percent chance the high valuation player will win in this case, and his net gain would be $3 million, his expected gain is $1.5 million. Similarly the net gain to the low valuation player conditional on winning is only $1 million, so the expected value of both bidders submitting a price of $1 million is $0.5 million to him. The other matrix entries are completed in a similar fashion.

Game 8.11: Second price sealed bid auction in free form

There is an object for sale (i.e. a cell phone). There are n players in this auction (n=3, 4,6). Each subject has a private valuation for the object that is drawn from a uniform distribution with minimum 50 and maximum 150. Each subject sees its own private value and submits a bid. When all the bids are submitted the highest bidder wins the auction and pays the second highest bid. The profit the winning bidder is the valuation minus the price.

Game 8.12: E-bay auction in free form

The difference from the sealed bid auction. The auction lasts t minutes. Each player sees the highest outstanding bid. When the time runs out the highest bidder wins the auction and pays the second highest bid plus one dollar.

Game 8.13: Amazon.com auction in free form

The auction last t minutes. However if you submit the bid in the last x seconds the auction continues for the next x seconds. The highest bidder wins the auction and pays the bid,

Game 8.14: Second price sealed bid auction in strategic form

As before suppose there are only two bidders, one of whom has a valuation of $4 and the other a valuation of $2. A strategic form for the second price sealed bid auction can be depicted in a similar way to the first price auction, by modifying the previous example to take account of the new bidding rule. Thus if the high valuation player bids $5 million and the low valuation player bids less than that, then the high valuation player wins the auction and pays the bid of the low valuation player. Similarly if the low valuation player bids $3 million then the item is sold to the high valuation player for $3 million for a gain of $1 million. Inspecting the cell corresponding to the (bid $4 million, bid $5 million) strategy profile, we see the payoffs are ($0, $1 million) as required.

Game 8.15: More than one weakly dominated strategy

There are three strategies for row player (Alpha): U, M and D and column player (Beta) has two strategies L and R. U and M are weakly dominated by D for Alpha. This example demonstrates that, in contrast to the iterative removal of strictly dominated strategies, the solution found by iteratively removing weakly dominated strategies is path dependent.