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We assume that an event was reported to one of robots, and a response by one robot is required. The goal of robot-robot coordination for task assignment is to select the best robot for responding to a reported event so that communication cost for selecting, and response time for performing the task are minimized. Existing solutions, except those recently proposed in, are either centralized, neglecting communication cost, assuming complete graph, or based on flooding with individual responses to robot decision maker (simple auction protocol - SAP), ignoring communication cost and response time bound. This article proposes greedy improvement to previously proposed (in) k-hop simple auction protocol (k-SAP) and k-hop simple auction aggregation protocol (k-SAAP) for task assignment in multi-hop wireless robot networks. After decision about the best robot is made by k-SAP or k-SAAP, new 1-SAP greedy auction is initiated by that robot in order to search for possibly better robot in 1-hop neighborhood. Such greedy approach proceeds until no better robot is found. Improvement of new k-SAPG and k-SAAPG over k-SAP and k-SAAP by applying greedy approach is shown by simulation results.