Software Maintenance is becoming more and more challenging due to rapidly changing customer needs, technologies and need for highly skilled labor. Many problems that existed a decade ago continue to exist or have even grown. In this context organizations find it difficult to match engineer interest, skill to particular customer problem. Thus making it difficult for organization to keep the selfish and rational engineers motivated and productive. In this thesis we have used game theory and mechanism design to model the interactions among such selfish engineers to motivate truth revelation using incentive based allocation schemes for software maintenance problems, especially Ticket Allocation Problem. Ticket allocation or problem allocation is a key problem in the software maintenance process.Tickets are usually allocated by the manager or the technical lead. In allocating a ticket, the manager or technical lead is normally guided by the complexity assessment of the ticket as provided by the maintenance engineers, who are entrusted with the responsibility of fixing the problem.The rationality of the maintenance engineers could induce them to report the complexity in an untruthfulway so as to increase their payoffs.This leads to non-optimal ticket allocation. In this thesis we first address the problem of eliciting ticket complexities in a truthfulway from each individual maintenance engineer, using a mechanism design approach. In particular, we model the problem as that of designing an incentive compatible mechanism and we offer two possible solutions.The first one, TA-DSIC, a Dominant Strategy Incentive Compatible (DSIC) solution and the second solution, TA-BIC, is a Bayesian Incentive Compatible mechanism. We show that the proposed mechanisms outperform conventional allocation protocols in the context of a representative software maintenance organization. In this thesis,we next address the incentive compatibility issue for group ticket allocation problem .Many times a ticket is also allocated to more than one engineers. This may be due to a quick customer delivery(time)deadline. The decision of such allocation is generally taken by the lead, based on customer deadlines and a guided complexity assessment from each maintenance engineer.The decision of allocation in such case should ensure that every individual reveals truth in the proposed group(or coalition) and has incentive to participate in the game as individual and in the coalition. We formulate this problem as Normal form game and propose three mechanisms, (1)Division of Labor, (2)Extended Second Price and (3)Greedy Division of Labor. We show that the proposed mechanisms are DSIC and we discuss their rationality properties.