Dollar Auction Game

The movie "War Games" produced in the late 80s concludes with the protagonists reaching the stunning realization that the only way to win in the game of nuclear war is not to play the game in the first place. The Cold War was yet to be concluded then and people still lived under the cloud of unease that a nuclear war would end it all for the human race. With perfect hind-sight one wonders if there was any point in the whole exercise of building incredible nuclear arsenals to obtain a balance of terror in the game aptly called MAD--mutually assured destruction. But games nations play often do not lend themselves to rational explanations. Individuals too can exhibit irrational behavior or at least they may seem to be irrational until one examines the structure of incentives that people face.

One enlightening model of human behavior is the so-called "Dollar Auction" which illustrates the sort of trap that conflicts can lead to with costly consequences. This auction proceeds much as a normal auction except that while the highest bidder gets to keep the $1 bill bid upon, the second highest bidder has to pay the auctioneer the amount of the second highest bid.

This game played at a party leads to some unexpected outcomes which result from the dynamics of conflict escalation. Players exhibit irrationality in most cases and often the $1 bill is auctioned off for many times its value. This happens because there is a trap in the structure of the game where the loser not only does not get the prize but also loses the amount he bid.

Suppose the auction begins with a bid of 5 cents. This is appealing to most since 5 cents is worth bidding for a prize of a dollar. But as the bidding proceeds beyond 50 cents, the players are caught in a trap. At this point the game changes complexion. Assuming that bids have an increment of 5 cents, the person with the bid of 50 cents has an incentive to outbid the higher bid of 55 cents. Otherwise he would lose 50 cents and the winner would gain 45 cents. Naturally, the bidding continues upwards. The auctioneer from this point onwards stands to gain irrespective of what happens next. When the highest bid is 95 cents, the situation is not at all rosy for the second highest bidder. He stands to lose 90 cents if he stops there. He also knows that his opponent stands gain 5 cents. Therefore the bid reaches $1. The participants quickly realize that it is no longer a game in which either of them would win. The question from then on is whether one can stand to see one's opponent lose less than oneself. Because at this point both lose money but the "winner" loses a dollar less than the loser. The only winner in this game is the auctioneer.

What are the modes of termination of the dollar auction? First, the players could realize right up front the nature of the trap and refuse to participate. No one loses and the auctioneer doesn't gain anything. Once the auction starts, it is still possible for the players to exit without losing. This happens if the players collude and decide to not outbid each other and to stop before the highest bid reaches 50 cents. They could agree to split the profits among themselves. And the auctioneer loses money in this deal. This scenario does not occur because co-operation requires accommodating one's opponent's interests which may be inconceivable in a situation of escalating conflict. Once past the 50 cent mark, the auctioneer is assured of a profit. The game continues till one of the participants exhausts his capacity to bid any more or one decides to cut his losses and fold. The winner is of course not as badly off but still has the winner's curse of having paid more than the value of the prize to win the prize.

The only way to win at a dollar auction therefore is either to not participate or if one does begin, then to either reach a compromise with one's opponent or to exit as early in the game as possible.

Wars too have the peculiar characteristic that both parties, winner as well as the loser, pay. The dollar auction game illustrates the trap that nations fall into in a process of conflict escalation given the structure of strategic games.

The dollar auction is a perfect model of the conflict that India faces against Pakistan, with Kashmir being the dollar being auctioned. The bids in this auction are the military expenditure of each nation and the auctioneer is the one who collects the spoils of the military expenditures of the two nations. Since advanced industrialized countries are the major suppliers of arms, they play the role of the auctioneer quite well.

Models are abstractions of the real world and their utility derives from their ability to predict outcomes that obtain in the real world and to the extent that they explain observed behavior, they are useful. Does the dollar auction model explain the observed behavior of the participants of this Kashmir conflict? Consider the motives of the auctioneer in the model. The auctioneer has an incentive to see that the conflict is not terminated. The imminent bankruptcy of one of the participants could end the game. The auctioneer could offer to lend money to the party on the verge of bankruptcy and at the same time encourage the other party to continue with the bidding. The recent IMF loans extended to Pakistan is an instance of this move in the real world that the model predicts. The intervention of the AICs to end the conflict would be parallel to the auctioneer, contrary to his interests, stopping the bidding game. This would not happen in the model and it does not happen in the world it attempts to model. One could be puzzled by the seeming irrationality of the IMF lending money to Pakistan while at the same time the AICs agreeing that India is the aggrieved party. All puzzlement disappears once one notices that this strategy precludes the possibility of the game ending too soon.

Nations are not monolithic entities. They are comprised of groups with different incentives and interests. Even in the so-called developing world there are groups whose interests align more closely with corresponding groups in the advanced industrialized countries. Politicians and arms dealers in poor countries stand to gain as much from conflict escalation as do the owners of the military-industrial complex of the advanced industrialized countries. The crowds who stand at the sidelines and cheer on the combatants are the leaders, the commanders, and the arms manufacturers of all the countries that are in the conflict as well as those that just supply the arms. The average citizens in both the countries stand to lose not just in terms of human lives but also in terms of a lower standard of living necessitated by the hardships imposed on them to pay for the military hardware bought from the AICs.

In a recent op-ed piece titled "Stopping America's Most Lethal Export" in the New York Times, winner of the 1997 Nobel Prize Oscar Arias wrote: "While the arms industry profits, people throughout the world suffer... the true weapons of mass destruction are the jet fighters, tanks, machine guns and other military exports that the United States ships to non- democratic countries--a record $8.3 billion worth in the 1997 fiscal year, the last year for which figures are available." Aside from anything else, the incontrovertible fact is that war is costly for all except for weapons manufacturers.

Kashmir has been immensely costly to India and in all likelihood Kashmir would ultimately kill the already crippled Pakistan. While India is likely to win in the end, it would have paid way too much in terms of blood, sweat and tears. The problem is that India played the game somewhat like a novice playing the dollar auction--raising the bid by 5 cents each time.

If the more powerful player in the dollar auction goes to the other in the initial stages of the game and makes a credible commitment of setting aside an amount greater than the amount the other can ever bid, then the second player would find it rational to not bid at all. This would be so because the second player knows that not only will he lose for sure, but that it will be a fatal loss. This way, the first player not only does not have to spend the money set aside but actually wins the dollar for just 5 cents. The winner has to make a credible threat to ruin the other party. Any vacillation on the part of the stronger party would preclude this outcome.

India should have announced that it was willing and capable of outbidding Pakistan on the issue of Kashmir irrespective of what Pakistan could ever afford to bid. A credible announcement does not necessarily amount to actually spending the outrageous amount; it only requires the demonstration of the will to do so if the contingency arose.

However, now the game is at a stage where each country has already bid an amount greater than the value of the prize. There are two outcomes: one, the game ends with Pakistan going bankrupt; or two, India and Pakistan negotiate an end to the conflict with the border status quo ante. It is unlikely that the interests that stand to gain from continued conflict would allow the first possibility. Every time Pakistan appears to be taking its last gasp, resuscitation in the form of financial aid would appear either from the AICs or from oil-rich Islamic countries. The second scenario is unlikely unless India makes it very clear that it is willing to risk losing a large number of its citizens in a nuclear attack by Pakistan.

Either way, India will suffer the winner's curse of having paid too dearly for the prize. As in the movie War Games, the only way to win is to not play the game in the first place.