Experimental Findings and Comparative Analysis 126

The experimental analysis targets the algorithmic simulation and comparison between the GSPM and EM for the matching allocation and pricing outcomes of the CAP class of multiple units DA of a single-item (i.e., e-service). The single items (e-services) may be constructed from multiple attributes and multiple Q-levels using the RBBL tree based bidding attribute-values and logical rule and operators formulae. The simulation allows for repetitive trades. Requests and asks bids are either bounded or unbounded by the Min/Max request and ask bid limits. The simulation implements, analyses and reports the algorithms and the experimental findings of the presented GSPM and EM DA mechanisms that serve either bounded or unbounded bidders of single or multiple Q-level request and ask bids. The DA mechanisms exploit the conveyed RBBL instance of the bidders that dictates their rational reactions at constant learning.

The experimental scenarios examines the performance advantage of using only the rules aggregation for a number of request and ask bidders with the assumption that bidders apply self-learning abilities at repetitive trades that maps to logical rules and conveyed to the FX. The RBBL rules aggregation inside the free exchange reduces the relative processing time of the remote (i.e., over local networks) bidder agents processing time in multiple folds. Furthermore, the reduction of processing time by the aggregation of rules increases significantly with thicker e-market trades over best effort internet. In addition, our work assumes that the smart deduction and minimal elicitation, that is to be explored in future work, would have a substantial performance improvement for more rapid trades.

The FX applies the GSPM matching on the induced and generated e-services and requests and asks bids to find an efficient and stable matching allocation and pricing outcomes. The FX e-marketplace facilitates truthful interactions by implementing the GSPM double auction matching that exploits the multiple Q-level forward and reverse GSP double auctions for e-trading e-services. The GSPM DA delivers stable social efficiency quite rapidly at the first trades with fairly thick e-market trades (i.e., more than 100 bidders). However, the EM DA keeps unstable social efficiency for most repetitive trades. The GSPM stable efficiency is due to the pricing rule that narrows down the tactical maneuverability, the multiple Q-level cross-matching and the best response at repetitive trades. In fact, the rational reaction of bidders at constant learning of the e- market dynamics drives both the GSPM and EM to converge to stable efficiency. The process transforms the exchange e-market from incomplete information to complete information truthful settings. However, there is no guarantee the EM DA would converge in a lower number of rounds due to the EM pricing model that allows for aggressive tactical moves of losers throughout repetitive trades until they converge to the EM prices. The GSPM DA secures the e-market profitability that grows with thicker trades. This is an inherent attribute of the GSPM DA matching. However, the EM DA mechanism delivers no profitability. The e-market profitability is lucrative to e-marketplaces that deliver the liquidity and the computational e-services. The bounded GSPM and EM DA converge to the maximum number of matched pairs close to the true value matched pairs. This is the natural matching progress of the bounded bidders at repetitive trades. The unbounded GSPM and EM DA converge, however, to the maximum full matched pairs that cover almost all ask-bid pairs at repetitive trades. This is a result of the unbounded reactions of bidders that scarify risk neutrality for a wining match. The unbounded GSPM DA and EM DA allows for negative utilities due to the unbounded aggressive adjustments of losers that direct the convergence of the risk unneutral higher value request bids and lower ask bids of the losers until they turn into winners. This is due to the violation of the risk neutrality by the losers over true bounds. Otherwise, the bounded conservative conduct of winners targets utility maximization. Our work examines the

unbounded model to investigate bidder’s behaviours at GSPM thicker and/or repetitive trades. An interesting observation is that GSPM DA delivers stable AE social efficiency for bidders of bounded GSPM trades and also for winners of unbounded GSPM trades. The losers of unbounded GSPM trades destabilises their allocation region due to their unbounded aggressive moves that breaks risk neutrality.

It is also observed the variance of both GSPM and EM DA requests and asks drops rapidly at the initial trades due to the bounded or unbounded large delta adjustments of the requests and asks of losers aggressive moves. The variance converges, then, with rather the smaller adjustments of winners conservative moves to a stable low value as bidders hit their true valuation bounds or as the difference between the falling bids and the rising asks narrows down until they get closer to the GSPM second prices in order or the EM Mth price bounds.

The complexity analysis of the diverse GSPM DA mechanisms examines the processing runtimes at diverse GSPM and EM trades. Our work observed there is at no extra computational cost in implementing the GSPM algorithmic heuristics compared to the EM DA counterpart. In fact, the GSPM mechanisms utilize the EM algorithms for the sorting, grouping, indexing and the allocation matching that often demands the highest computation cost while applying linear pricing models. Hence, the GSPM DA would deliver better economic properties such as stable efficiency and e-market profitability for the same computational cost.