Showcase Bid Calculator

Asheville, North Carolina, USA

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• Bidding Range

• Optimal Bid

• Expected Payoff vs Opponent

• Expected Payoff vs Pool

18000

30030

17363

16533

18000

30030

17363

16533

Iterations to Equilibrium: 7

This showcase bid calculator was developed to accompany the article "Analysis of *The Price is Right* Showcase Round: Bid-Shading Strategies for Players of Arbitrary Skill" by Craig H. Collins, submitted to the MDPI journal *Games*. Please refer to that article for a full discussion of the problem, assumptions and solution.

The purpose of this calculator is to return optimal bids and corresponding expected payoffs for the contestants in the Showcase Round of the TV show *The Price is Right*. One may select a Complete Information version of the game or an Incomplete Information version, as described below. These versions differ in terms of the knowledge each player has about her opponent's estimating skill.

A player's estimating skill is defined here as the maximum difference between her valuation of the showcase and its actual price. For example, if a player's estimating skill is +/- 20% and she thinks her showcase is worth $30,000, then the actual price will turn out to be somewhere between $24,000 and $36,000 (for a *bidding range* of $12,000). The calculator assumes that all prices in that range are equally likely and that the actual showcase price will not fall outside that range.

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Whichever type of game you select, you must enter the minimum and maximum possible showcase prices (10000-99999 without commas). These values are hard limits -- the actual showcase price will not fall outside this range -- and both players are assumed to know these limits. In the 2017-2018 season, the least expensive showcase was $20,406 and the most expensive was $60,676.

In the Complete Information game, each player knows her own estimating skill, the skill of her opponent, the valuation of her own showcase and her opponent's valuation of her opponent's showcase. In this version, unlike the television show, there is no choose-a-showcase step, and the bids are made simultaneously, not consecutively, so neither contestant knows (without using this calculator) what her opponent will bid.

For the Complete Information game, enter each player's estimating skill, expressed as a plus-minus percent (1-99%) of her showcase valuation, then enter the valuation of each showcase (10000-99999 without commas). The calculator returns each player's optimal bid and her expected payoff in this matchup. The expected payoff is the amount that a player would collect per game, on average, if she were to play the same game against the same opponent multiple times.

Although the calculator checks and corrects most entries in real time, be sure to click the CALCULATE button to validate the entries and results.

In the Incomplete Information game, each player knows her own estimating skill but not that of her opponent. But the players do know the distribution of skill-levels in the player pool. These are called *player-types*. Each contestant must be one of the defined types. You may define up to five player-types.

For the Incomplete Information game, begin by entering the estimating skill for each player-type in the pool, expressed as a plus-minus percent (1-99%) of showcase valuation, then enter the percent (0-99%) of the player pool that is of that type. Enter 0% to exclude a given type from the pool.

After defining the pool, enter the estimating skill and showcase valuations for the contestants in this particular matchup. (Remember, the contestants do not know their opponent's type beforehand.) The estimating skill that you enter for each contestant must match the skill of one of the active types in the pool.

The calculator returns each player's bidding range, her optimal bid against the player pool, and her expected payoffs against her specific opponent-type and the pool, if she were to play against the same pool of players multiple times and her opponents were randomly selected from the pool.

Finally, the calculator reports how many iterations were required to find the equilibrium bid set for this set of player-types and showcase valuations. Equilibrium is reached when none of the best-response bids by any player-type differ by more than a dollar from the previous iteration.

The calculator checks and corrects user entries in real time to make sure that the Percent of Pool entries sum to 100 and that the estimating skill of each contestant matches one of the defined player-types. Be sure to review your entries and then click CALCULATE to validate the entries and results.