others, etc. This means that the values v should probably not be the same, but they probably are more closely related than a uniform distribution: after all, at a base level it is the same object being pursued. We can generalize the formula to incorporate this idea. For an unknown probability distribution of values, f with cumulative distribution function F , 4 ݏ ሺ ݒ ሻ = ܨݒ ିଵ ሺ ݒ ሻ − ܨ ିଵ ሺ ௩ ௩ ݒ ሻ ݒߜ (7) Another issue that needs to be dealt with is that of information. The above model assumes no information is available to the players about each othersÊ planned strategies. In an office environment, however, you would likely be able to see what other employees are doing. This can have a significant effect on othersÊ strategies. For example, if you see someone working harder for the promotion than you ever would consider worthwhile, you would be advised to put in a bid of 0 effort. 5 This can end up ÂstreamliningÊ the competition – it ends up with most players dropping out, leaving a few of the potential highest bidders behind. This ends up with a final battle between a few players. In the real world people are often loathe giving up in a situation when they have large Âsunk costsÊ. This could, in terms of the all-pay auction, create a Ârace to the bottomÊ between the final players. This is good for the employers clearly, but not necessarily for participants. In fact, the Nash equilibrium described earlier would not be possible with full information about each otherÊs bids. When deciding and announcing what bids one is going to make, each person would rationally only bid slightly above the next highest bid. People would keep saying they are going to bid just a bit higher than the last until the person willing to bid the highest is at the top of the pile, at which point everyone else would have pulled out of the bidding. In an all-pay auction, if you know someone is going to put in a higher bid than you it would be optimal to bid 0, otherwise your bid will go to waste. Often we see, however, in such competitive environments, people try and ÂhideÊ how much effort, what ÂbidÊ, they are putting in. The more information your opponents have on your strategy the more they can strategize, and the worse it is for you. As a response, however, many will also hide their information from you. It seems as if another game is being played to decide how much information is revealed. In general the hiding of information means that people are able to make less strategic (less optimal decisions). This all resembles the PrisonerÊs dilemma, every individual worker would be better off if all information was available, allowing them to make a more informed decision. The company may, however, have some interest in creating a little uncertainty, which in reality could often lead to overbidding. Alternatively more information available may stoke the competition and promote a more intense battle: it all depends how much behavioural aspects drag peopleÊs strategies away from the classical game theoretic strategies. Another assumption made was that the promotion was decided only on how much effort each employee puts in. It is certainly true that effort put in is one significant factor, but others, such as natural skill and luck have a good say as well. If there were an employee who clearly has a great deal of natural ability at his job, this could have significant effects on the strategies others should use. This situation would be rather like one where a bidder is able to make a larger bid, without having to pay all the costs. This would not maximize the employeesÊ input, which is bad for the employers. For this reason (but also because they simply do have to fill multiple positions) multiple ÂprizesÊ can be awarded. The Âexclusion principleÊ 6 states that it could in fact be worth an employerÊs time to ÂexcludeÊ their best employees from such competitions. This may 4 http://www.stanford.edu/~jdlevin/Econ%20286/Auctions.pdf (date accessed 29.07.13). 5 Baye, Michael R., Dan Kovenock, and Casper G. Vries. ‘The All-pay Auction with Complete Information.’ Economic Theory 8.2 (1996). Print.
6 Clark, Derek J., and Christian Riis. ÂCompetition Over More than One Prize.Ê The American Economic Review 88.1 (1998). Print.
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