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# Game Theory Analysis

Document Type:Coursework

Subject Area:Economics

Document 1

The incomplete information in an auction is due to the fact that in many auction processes, one party possesses information that is related to the transaction which the other bidder does not (Chatterjee et al. This implies that each bidder in an auction knows his or her value attached to the product or item. Auction bidding can take several strategies and dimensions but share one major characteristic of universality and can be used to purchase or sell products (Mago &Pate 2009). In many instances, the result of a bidding process is independent of the bidders’ identity and thus anonymous. Recently, auctions have been brought to the everyday lives of individuals through the internet in sites such as eBay (Fatas and Manez 2007). In many cases, private model auction works with the assumption that all the values or estimates are independent to all the bidders.

On the other hand, the common value model often works on the assumption s that the values or estimates are independents only up top known variables of probability function. The affiliated value model is another general type of strategic bidding where the total utility of the bidder depends on the private signal of individual and some values which are unknown. Both the common and private models are argued as the extension of the general affiliated framework. In making the assumptions regarding the value of distributions of bidders, most of the research studies work on the assumptions of symmetric buyers. According to Murota (2016), it is necessary for the equilibrium to be obtained in a bidding process. Achieving the equilibrium implies that the sellers annd the buyer have the perfect knowledge and information regarding the value and cost attached to the item being sold (Colman 2016).

However, the research study by Cheng et al. (2016) contradicted the notion that equilibrium should be achieved in the auction market. In support of this argument Samuelson (2016) stated in his game theory research that bidding process is characterized by incomplete information thus it is impossible to have equilibrium in the auction market. W(b) = Pr {b2 less than b} n-1 Which is given as [n/(n-1)]n-1 bn-1 Also, the anticipated pay-off and the probabilty of win for bidder 1 is given as follows U(b) is given as w(b)(v-b) This can be expressed as {n/(n-1)n-1bn-1(v-b) Which finally bacomes (n/(n-1))n-1 (bn-1v-bn) From the above equation it is evidently confirmed that through the differentiation of U9B) taking on is maximun at B (v) = ( n-1)/n)v.

This shows that the B(v) is the a unique symmetric equlibriums as indicated by the emprical research by Su et al (2016). As a result, it can be concluded that theree is unique equilibrium in the bidding process. Analysis of Auction with Regards to Known and Unknown Values Generally, auctions are used by the sellers of the items in situations where they lack appropriate estimate of the true value of the buyers or bidders of the items sold. Also, it is used in cases where the bidders do not have an idea or know the values of other bidders in the process of auction. This means that there is no need for auction for the seller since he gets as much as he or she could reasonably expect from the sale by just announcing the fixed price.

The scenario where there is complete information of the value attached by the buyers in the bidding process demonstrates symmetric information. Such cases can imply that the process of an auction is irrelevant and thus no need for the bidding process. In game theory, it should be noted that each of the players has unknown strategies that they use to win. As a result, the situation where the seller has complete information on the value that each bidder attaches to the item on sales is against the game theory of auction. The players in the bidding process consist of the buyers and sellers. Each of the players in the bidding process has a specific bidding strategy that is unknown to others.