TV Channel Auction with Multiple Identical Permits
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This is supposedly a real TV channel auction that happened in Greece two weeks ago described in the Reddit post linked above. The channel is auctioning off 4 identical permits to 8 participants. Each participant has a value Vn for a permit, and can only acquire 1 permit. Participants don’t know other participants’ values. The government has to decide how to design the auction while keeping it fair and while maximizing profit. How the government designed the auction was with a relatively complicated scheme involving multiple rounds within multiple phases. Sometimes, the best strategy for an auction designer is to make the auction so complicated that people are more likely to act irrationally. However, we can connect this to class by talking about whether a simple 4-round (one for each permit) ascending bid, descending bid, first price, or second price auction is the best auction type for this problem in order to maximize profit.
In each round, 1 permit is up for auction and 1 participant will win the permit. In rounds 1, 2, and 3 each participant has to think about whether or not they want to bid less in order to take their chance at step 4. We can simplify the problem to one that we talked about in class with only one item up for auction and no future items. In round 4, there are 5 participants remaining due to 3 participants winning in rounds 1, 2, and 3. As talked about in class, if the auction is ascending bid or second price, the optimal bid is one’s value. If the auction is descending bid or first price, one should probably bid less than one’s value. A Nash Equilibrium is bidding (N-1)/N = 4/5 times one’s value.
What about in round 3? Now each player has to decide how to bid while knowing that if they don’t win in this round, they can still try to win in round 4. There are 6 participants in round 3. In all four auction types, if a player thinks that they might be able to get a better payoff (value minus price paid) in step 4, they might bid less/throw this auction in order to play in step 4. For example, if the auction is ascending bid or second price, one’s payoff if they win depends on the highest bid of everyone else. This means that the payoff depends on what another player bids. In step 3, if a player thinks that they might have the highest bid and that the highest bid of everyone else is going to be lower in step 4 than in step 3 (for example, if one thinks they have the highest value, and the participant with the next highest value winning in step 3 would cause step 4’s next highest value to be lower), they might bid lower in order to avoid winning in step 3. However, if everyone does that, that creates a huge incentive to bid at least moderately because everyone else is bidding low, which increases one’s potential payoff. This auction probably doesn’t have a pure Nash Equilibrium and has a mixed Nash Equilibrium instead.