▼ Electricity markets face multiple challenges such as intermittent electricity generation, high levels of average prices, and price volatility. Moreover, future electricity generation is required to be environmentally friendly, reliable and affordable. This thesis presents game-theoretic frameworks for addressing the aforementioned challenges in electricity markets. In our simulations, we apply and evaluate our developed competitive electricity market models to Australia's National Electricity Market (NEM). We extend an existing Cournot-based wholesale electricity market model by considering strategic storage players in addition to generation and transmission players. This allows us to model the strategic behavior of storage players in future electricity markets, which can significantly help to reduce the price volatility. The problem of high levels of price volatility in electricity markets might be related to the closure of base-load coal power plants or the fast growing expansion of wind power generation. Using our Cournot-based model, we design a storage allocation framework to find the optimal regional storage capacities to limit the price volatility in the market to a certain level. The results show how the impacts of strategic and regulated storage firms differ in reducing the price volatility in the market. We next study the market power problem, which is one of the main contributors to high levels of power prices and price volatility in electricity markets. We develop an optimization model for allocating a fixed budget on regulated wind and storage capacities to increase the competition and reduce the weighted sum of average price and price volatility in an electricity market. The results indicate that storage is more effective in price volatility reduction than wind, whereas wind is more efficient in average price reduction. We then study the tax and subsidy policies which can lead to emission reduction and reliability enhancement in electricity markets. We extend our developed Cournot-based electricity market model as a long-term generation expansion model with an upper bound on CO2 emission in the market. In addition to the future generation capacity portfolio, this model proposes the carbon tax levels required to achieve the carbon abatement target in the market. The policies imposed in electricity markets for emission reduction targets may lead to large investments on intermittent renewable energies. Designing a low carbon and reliable electricity market, we develop a long-term market expansion model with emission reduction and dispatchable capacity constraints. The model is used to calculate the tax and subsidy on CO2 emission and fast response dispatchable capacity, which can lead to transition towards a green and reliable electricity market in Australia.

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In this thesis, we focus on the rationing polices for the hotel room inventory control problems. Our study begins with a brief overview of revenue management in hotel industry, emphasizing the importance of room inventory control in revenue management problems. Mathematical models for controlling the room inventory in the literature are then reviewed along with recently developed game theoretic applications in revenue management. In game theoretic context, we establish three types of models to solve the hotel room inventory control problem in three different situations: 1) two-player two-fare-class static single-period game with complete information; 2) two-player two-fare-class dynamic multiple-period game with complete information; and 3) two-player two-fare-class single-period game with incomplete information. In the first situation, we find the existence of unique Nash equilibrium and Stackelberg equilibrium in the non-cooperative case. We provide the exact forms for these equilibria and corresponding conditions. Next, under the dynamic game settings, we provide the sufficient conditions for the unique Nash equilibrium. In the last situation, we consider the static single-period games with incomplete information and discuss the optimal strategies for the uninformed case, secret information case, private information case and public information case. The unique Bayesian Nash equilibrium in each case is found. We then analyze the values of different types of information and study their relations in different situations. Under each game theoretic setting, we present the managerial implications of our solutions along with the numerical examples. The thesis is concluded by a discussion of how game theory can is useful in hotel industry, and its relationship to other topics in revenue management.

Thesis

Doctor of Philosophy (PhD)

Advisors/Committee Members: Parlar, Mahmut, Business.

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"This thesis is presented for the degree of Doctor of Philosophy"

"September 2011 (original), September 2012 (with corrections)"

Bibliography: leaves 153-156.

1. Trading in uncertainty  – 2. Literature review  – 3. Generic opponents model  – 4. Random parameters model  – 5. Adaptive model  – 6. Tree based contextual coefficients  – 7. Deployment  – 8. Results  – 9. Conclusions  – Appendices

The focus in this thesis is on the mathematics underpinning the system rather than details such as how to decode on-line sites. What now follows is a summary of the thesis in more detail: Much of the research into poker has built on the concepts developed by Von Neumann [27] and Borel [4]. Game Theory concepts have been developed and used in conjunction with cutting edge techniques such as Neural Networks to develop playing algorithms in a similar way to which games such as Chess or Checkers have been solved. These techniques are not necessarily gambling related, even though poker is usually played as a gambling game. The problem with the Game Theory approach is that analysis of full scale poker rapidly becomes intractable. Prominent researchers in the Game Theory approach ([3], [18], [21],[20],[2], [1]) have recognised this and much of the subsequent research has centred around reducing the size of the problem to be solved. Derivation of a Game Tree for a reduced problem was also the approach adopted by von Neumann and Borel. This approach has been successful and can be summarised as finding an exact solution to an approximating problem. Methods seeking approximations to the full problem that retain the properties of the real problem have been developed and are ingenious. In this thesis a different approach has been used. Instead of seeking approximating problems which may be solved exactly, approximate solutions to the full problem are sought. Regression techniques have been used to find approximate solutions to the full problem. Rather than try to tune a strategy engine using Neural Networks to solve the problem in a human-like way, the population variance in preferences (as measured by coefficients) has been measured and past data for given contexts is used to estimate where on the population distribution of preferences a particular context resides. The resulting system still "learns", but in a different way to a Neural Network. The play has been reduced to a sequence of actions which are chosen to maximise profit expectation. This has much in common with financial market trading where a sequence of trades is likewise chosen to maximise profit. The Game Theory approach also maximises profit expectancy, but because that approach necessitates analysis of a computationally intractable Game Tree, the expectation actually maximised is that of an approximating problem. In a sense the approach adopted here is the opposite of the approach adopted by the authors mentioned above in that they seek exact solutions to an approximating problem whereas this research seeks approximate solutions to the exact problem.

1…

Advisors/Committee Members: Macquarie University. Department of Statistics.

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SOME SMALL EUROPEAN COUNTRIES HAVE TRIED TO STABILIZE THEIR ECONOMIES IN THE LAST DECADE AND THEIR EXPERIENCES OFFER VERY USEFUL LESSONS. ALL THESE COUNTRIES ARE EXTREMELY OPEN AND SMALL IN TRADED GOODS MARKETS TO HAVE ANY IMPACT ONDEVELOPMENTS IN THE REST OF THE WORLD. TWO ISSUES HAVE BEEN STUDIED IN THIS DOCTORAL DISSERTATION. THE FIRST HAS TO DO WITH THE STABILIZATION OF OUTPUT AND PRICES. MORE PRECISELY, WE INVESTIGATE WHETHER STABILIZATION POLICIES COULD INCUR DISINFLATIONARY EFFECTS AND EXPANSIONARY EFFECTS ON REAL MACROECONOMIC AGGREGATES. THE SECOND ISSUE OF THE DOCTORAL DISSERTATION DEALS WITH THEPOLICYMAKERS' ATTITUDES TOWARDS DEBT STABILIZATION. TWO CRUCIAL QUESTIONS ARE ADDRESSED HERE: (I) IS THE PATTERN OF DEBT SUSTAINABLE? AND (II) DOES THE FISCAL AUTHORITY DOMINATE OVER THE MONETARY AUTHORITY IN THE DEBT STABILIZATION PROCEDURE OR VICE VERSA?

ΜΕΡΙΚΕΣ ΜΙΚΡΕΣ ΕΥΡΩΠΑΙΚΕΣ ΧΩΡΕΣ ΠΡΟΣΠΑΘΗΣΑΝ ΝΑ ΣΤΑΘΕΡΟΠΟΙΗΣΟΥΝ ΤΙΣ ΟΙΚΟΝΟΜΙΕΣ ΤΟΥΣ ΚΑΤΑ ΤΗΝ ΤΕΛΕΥΤΑΙΑ ΔΕΚΑΕΤΙΑ ΚΑΙ ΟΙ ΕΜΠΕΙΡΙΕΣ ΤΟΥΣ ΜΠΟΡΟΥΝ ΝΑ ΑΠΟΤΕΛΕΣΟΥΝΧΡΗΣΙΜΑ ΜΑΘΗΜΑΤΑ. ΟΛΕΣ ΑΥΤΕΣ ΟΙ ΧΩΡΕΣ ΕΙΝΑΙ ΕΞΑΙΡΕΤΙΚΑ "ΑΝΟΙΚΤΕΣ" ΚΑΙ "ΜΙΚΡΕΣ" ΣΤΙΣ ΔΙΕΘΝΕΙΣ ΑΓΟΡΕΣ ΩΣΤΕ ΝΑ ΕΧΟΥΝ ΟΠΟΙΑΔΗΠΟΤΕ ΕΠΙΔΡΑΣΗ ΣΤΗΝ ΠΑΓΚΟΣΜΙΑ ΟΙΚΟΝΟΜΙΑ. ΔΥΟ ΘΕΜΑΤΑ ΜΕΛΕΤΩΝΤΑΙ ΣΤΗΝ ΠΑΡΟΥΣΑ ΔΙΔΑΚΤΟΡΙΚΗ ΔΙΑΤΡΙΒΗ. ΤΟ ΠΡΩΤΟ ΑΦΟΡΑ ΤΗ ΣΤΑΘΕΡΟΠΟΙΗΣΗ ΠΡΟΙΟΝΤΟΣ ΚΑΙ ΤΙΜΩΝ. ΠΙΟ ΣΥΓΚΕΚΡΙΜΕΝΑ, ΔΙΕΡΕΥΝΟΥΜΕ ΤΟ ΚΑΤΑ ΠΟΣΟ ΟΙ ΣΤΑΘΕΡΟΠΟΙΗΤΙΚΕΣ ΠΟΛΙΤΙΚΕΣ ΘΑ ΜΠΟΡΟΥΣΑΝ ΝΑ ΕΠΙΤΥΧΟΥΝ ΑΝΤΙΠΛΗΘΩΡΙΣΤΙΚΑ ΚΑΙ ΕΠΕΚΤΑΤΙΚΑ ΑΠΟΤΕΛΕΣΜΑΤΑ ΕΠΙ ΤΩΝ ΠΡΑΓΜΑΤΙΚΩΝ ΜΑΚΡΟΟΙΚΟΝΟΜΙΚΩΝ ΜΕΓΕΘΩΝ. ΤΟ ΔΕΥΤΕΡΟ ΘΕΜΑ ΠΟΥ ΑΠΑΣΧΟΛΕΙ ΤΗΝ ΠΑΡΟΥΣΑ ΔΙΔΑΚΤΟΡΙΚΗ ΔΙΑΤΡΙΒΗ ΑΦΟΡΑ ΤΗ ΣΤΑΣΗ ΤΩΝ ΣΧΕΔΙΑΣΤΩΝ ΤΗΣ ΟΙΚΟΝΟΜΙΚΗΣ ΠΟΛΙΤΙΚΗΣ ΕΝΑΝΤΙ ΤΗΣ ΣΤΑΘΕΡΟΠΟΙΗΣΗΣ ΤΟΥ ΧΡΕΟΥΣ. ΔΥΟ ΚΡΙΣΙΜΑ ΕΡΩΤΗΜΑΤΑ ΕΓΕΙΡΟΝΤΑΙ ΕΔΩ: (I) ΕΙΝΑΙ ΤΟ ΤΡΕΧΟΝ ΠΡΟΤΥΠΟ ΤΟΥ ΧΡΕΟΥΣ "ΔΙΑΤΗΡΗΣΙΜΟ" (SUSTAINABLE); ΚΑΙ (II) ΕΙΝΑΙ ΔΥΝΑΤΟΝ ΟΙ ΔΗΜΟΣΙΟΝΟΜΙΚΕΣ ΑΡΧΕΣ ΝΑ ΚΥΡΙΑΡΧΟΥΝ ΕΠΙ ΤΩΝ ΝΟΜΙΣΜΑΤΙΚΩΝ ΑΡΧΩΝ ΚΑΤΑ ΤΗ ΔΙΑΔΙΚΑΣΙΑ ΣΤΑΘΕΡΟΠΟΙΗΣΗΣ ΤΟΥ ΧΡΕΟΥΣ Η ΙΣΧΥΕΙ ΤΟ ΑΝΤΙΣΤΡΟΦΟ;

▼ Revenue Management (RM) is the practice of managing perishable assets by control-ling their availability and/or prices with an objective to maximize the total revenue. Seat inventory allocation falls in the purview of quantity-based RM. The liberalization of the aviation sector and the subsequent entrance of the low-cost carriers saw an ever-increasing customer base for the airline industry. Given the large number of buyers, firms were free to decide the price at which they would sell tickets. The low-cost carriers started to follow a third degree price discrimination and segmentation of the market, charging a higher price to the market with a relatively inelastic demand. Although a lot of work has been done in the area of seat inventory allocation under a monopolistic market scenario, we realized that not a lot of work had been done in a competitive market scenario. This thesis considers the problem of seat inventory allocation and pricing in a duopoly where each of the competing airlines have two fare-classes. We consider the possibility that the same fare-class may be priced differently by the two competing airlines and allow for the over flow of passengers between the airlines in the same fare-class. In the first part of our work, we develop a non-linear mathematical model for setting the booking limits for one of the two competing air-lines such that the revenue earned is maximized. We consider over flow of passengers from one airline to another in the same fare-class in response to a price differential and compare the results obtained from our model with the standard Expected Marginal Seat Revenue (EMSR) model under a monopolistic scenario. The results show that our model gives higher revenues than that obtained from the EMSR model. In the second part of our work, we consider a non-cooperative game between two competing airlines with price cutting as the strategy to increase their demand. Through numerical computations, we identify the pure strategy Nash equilibrium. From the results, we conclude that Nash equilibrium is achieved only when both the airlines follow the same pricing strategy indicating that individual price cutting will not be beneficial. This also indicates that unless the competitors enter into a cooperative coalition with each other, they would not benefit from deep discount offers. In the third and final part, we prove theoretically the existence of pure strategy Nash equilibrium in a two airline, two fare-class problem with price sensitive over flow of customers in the same fare-class that was computationally analysed earlier. The strategy / strategies at which Nash equilibrium is achieved are identified. We show that Nash equilibrium is only achieved when both the airlines price identically. Hence, our thesis concludes that differential pricing does not hold any significance for the competing airlines from an operational perspective. Advisors/Committee Members: Ramachandran, Parthasarathy (advisor).