Aa
Each bidder has a randomly determined private value for one unit of a good. Participants see the bids of others, and bids can be made until the end of the auction, as long as it is higher than the current highest bid. The highest bidder when time expires is the winner.
Learning Objective 1: Private-Value English Auction
Demonstrates the workings of a private-value English auction.
Learning Objective 2: Equilibrium Bidding Strategy
A player’s equilibrium bidding strategy is to bid as long as the current price is less than or equal to her value of the item after her bid.
Learning Objective 3: Relation to Other Types of Auctions
Play this game in conjunction with the first price private-value sealed bid auction (or the descending clock auction) to show the difference in optimal bidding strategy. You can also show that the optimal bidding strategy in the private-value English auction is equivalent to that of the second price private-value sealed bid auction (or the ascending clock auction).
Each bidder values one unit, and this value is by default drawn from the uniform distribution with Lowest Bidder Value=$10 to Highest Bidder Value=$100. Each bidder draws a new value for each new period if multiple rounds are specified (Periods > 1).
Each player has a weakly dominant strategy to bid up to her value. When the Current Price is greater than or equal to Buyer Value, the bidder should stop bidding.
Note: In order to increase the likelihood that a player can bid up to her value, make sure Price Increment= 1.
Suppose there are \(n\) bidders in the auction. Each bidder, \(i\), has his/her own private value, \(v_i\), for the good. In a private value game setting, the actual value \(v_i\) is known only to bidder \(i\). That is, for each bidder \(j\), he/she has imperfect information about what others™ value \(v_{i\neq j}\) might be.
In a private English auction, the standing bid is below a potential buyer's value, so there is an incentive for him/her to outbid the standing bid. Given the price increment \(b\), bidding over the standing bid by the least amount \(b\) is dominant for a potential buyer. Theoretically, bids should increase until \(v_2 -b\) is reached, where \(v_2\) is the second highest value among the set \(\{v_1, ..., v_n\}\). Nobody other than the buyer of the highest value has an incentive to bid over the current one. Thus, the final price should be somewhere in \([v_2-b\), \(v_2+ b]\). The highest valued bidder wins, and on average pays a price equal to the second highest among the bidders.1
The results highlight the Nash Equilibrium and show how close your students were to equilibrium play. Use the Go To: menu to switch between periods.
For each round, there is a table summarizing each group’s performance (Figure 1). The first columns display the highest item value (Optimal Surplus) and the winner's item value (Surplus).2 The final column shows seller Revenue (the winning bid). Check the radio button to reveal a figure summarizing a group’s bidding.
By unchecking the check-box for the Nash Equilibrium Bid Function, only markers that indicate bidder value and the final (highest) bid for each participant remain (Figure 2). The winning bidder is assigned a different marker from other bidders.
The equilibrium strategy in this auction is such that a player's highest bid does not exceed her value. A graph consistent with Nash bidding satisfies two conditions: 1) no bids above the Nash Equilibrium Bid Function, and 2) the winning bid belongs to the bidder with the highest value (i.e., the rightmost value in the graph.)
Our robot (i.e., an automated player) strategy is the following:
If the current high bid is lower than their value, the robot will increase the bid to a random number between the highest bid and a number halfway between their value and the highest bid.
Example
If the current bid is $50 and the robot's value is $70, the robot will raise the bid to a random number between $51 and $60.
1. Milgrom, P. R., & Weber, R. J. (1982). A Theory of Auctions and Competitive Bidding. Econometrica, 50(5), 1089–1122. ↩
2. Surplus calculations assume the items have no value to the seller. ↩
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