## The Price Is Right, the Travelers Dilemma and Markets

Imagine a twisted version of the show, The Price is Right where you are matched with a partner. You are competing to acquire the most amount of money at the end of the game. Each round you are allowed to name the price of an item, and if you name a price lower than your opponent, you make some amount of money. If you name a price higher than your opponent, you will face a penalty and lose some amount of money. Kaushik Basu in his piece “The Traveler’s Dilemma: Paradoxes of Rationality in Game Theory.” shows us that in this tv game show The Price is Right, the most logical price to name each item would be the lowest possible price value (which is 1 dollar in the show). This, according to Basu, is the only Nash equilibrium possible in the game.

Basu explains this theory by demonstrating that each player would assume that if they stated a price slightly lower than the other, they would be able to make more money than that person. This mentality follows to a finite point till they reach the lowest potential value point before they would lose money. In his example in the traveler’s dilemma, the Nash equilibrium would be (2,2) where each person would price their broken items to be 2 dollars. This is the most rational result according to Basu due to the process of backward induction. Backward induction, in the realm of game theory, is where you begin at the highest potential value and incrementally move towards the lowest point possible because you rationalize that your opponent will be doing the same. The end result of backward induction in this game, is two people with the lowest possible price value.

While this is the most rational result using game theory, it is very unlikely to happen, and it is mostly likely the case that the two players would know neither would go to the lowest possible price. When you take this out of context of a game and into the real world of business, this decision seems far more rational.

Imagine two companies who are selling the same item to the same target populations. They are both aware that the other is selling the same item and are strategizing how they should price the item so that they can make the most profits. Each company is not able to confer with each other on the price, but even if they do, they are not fully sure that the other company will keep its promise on the pricing of the item. If we ignore production costs and long term liabilities, the companies pricing becomes much more dependent on the theory described in the traveler’s dilemma. If one company prices their item higher than the other, they are more likely to have less sales than the other. This pushes each company to constantly push their prices down to the lowest possible price otherwise they would be losing out on business. When game theory is applied to the real world, the consequences of taking the rational choice becomes clearer.

https://www.jstor.org/stable/pdf/2117865.pdf?refreqid=excelsior:e1bcd123277034379177547ba60f1808

Basu, Kaushik. “The Traveler’s Dilemma: Paradoxes of Rationality in Game Theory.” *The American Economic Review*, vol. 84, no. 2, 1994, pp. 391–395. *JSTOR*, JSTOR, www.jstor.org/stable/2117865.