The problem of decision-making under uncertainty is addressed and a formulation in terms of payoff matrices is considered. A case study is investigated that involves three strategic alternatives and four possible weather scenarios: gains and losses are assessed through the sailing simulator and payoffs associated with choices are calculated. The most advantageous alternatives are selected through a maximization of expected utility. For this purpose, two possible decision-making contexts are considered: ‘decision-making under
risk’ and ‘under
ignorance’. In the first case, probabilistic information associated with outcomes are used, while the latter context involves considerations on the decider ‘attitude’ towards risk.
Further refinements to the model should undoubtedly be carried out in the future: this refers either to a closer modelling of yacht dynamics (e.g. when sharp course changes occur: quick manoeuvres, mark roundings) and to a refinement of the navigation module. In addition, interaction between yachts should be accounted for, so that decision trees related to racing
tactics (e.g.
blanketing, influence of right of way rules), could be investigated alongside with racing strategy.
Nevertheless, several applications can be envisaged for the simulator: as an example, interactive races could be set up and human choices recorded in order to provide a feedback on gains and losses due to personal decision- making schemata.
REFERENCES
1. Claughton A. R., Oliver J. C. III. Developments in hydrodynamic force models for velocity prediction programs. Proc. of RINA Conference ‘The Modern Yacht’, Southampton (UK), 2003. pp. 67-77
2. Todter C., Pedrick D., Calderon A., Nelson B., Debord F., Dillon D., Stars and Stripes Design Program for the 1992 America’s Cup. Proc. of The 11th CSYS, pp. 207-222
3. Keuning J.A., Vermeulen K.J., de Ridder E.J., A generic mathematical model for the manoeuvring and tacking of a sailing yacht. Proc. of The 17th CSYS, pp. 143-163
4. Masayuma Y., Fukasawa T., Sasagawa H., Tacking Simulations of Sailing
Yachts - Numerical
Integration of Equations of Motions and Application of Neural Network Technique, Proc. of The 12th CSYS, pp. 117-131
5. Harris D.H., Time Domain Simulation of a Yacht Sailing Upwind in Waves, Proc. of 17th Chesapeake Sailing Yacht Symposium, pp. 13-32
6. Roncin K., Simulation dynamique de la navigation de deux
Laboratoire de mécanique des fluides, ECN, 2002 7. Rousselon N. Prediction of hydrodynamic aerodynamic forces and moments, for use in a 4-
voiliers en interaction. PhD Thesis, and
S1 A1 – tack A2 - don’t tack
A3 - delay tack by 60 secs
S2 S3 66,40 S4
80,84 88,92 70,72 76,56 55,19 83,04 66,98 74,54 76,61 84,79
72,23
Table 5 - payoff matrix for awaref = 30° and tws = 4m/s S1
S2 A1 - tack A2 - don’t tack
A3 - delay tack by 60 secs
42,60 55,16 S3 28,95 S4 37,15
9,67 47,62 24,01 34,25 38,83 51,42 25,16 33,36
Table 6 - payoff matrix for awaref = 30° and tws = 6m/s S1
S2 A1 - tack
A2 - don’t tack
A3 - delay tack by 60 secs
69,22 80,3 8
37,97 63,70
72,8 3
74,9 2
S3
56,2 8
52,2 6
50,7 3
S4
63,2 3
61,9 4
57,6 7
DOF simulation tool, using a lifting surface panel code. MSc Thesis, Univ. of Southampton, 2005
8. Le Pelley D.J., Mancebo P., Smith R.P. A technical proposal for the design of an IACC yacht for the Year 2000, Ship Science Group Design Project Report, University of Southampton, 1998
9. Philpott A. and Mason A., Advances in optimization in yacht
performance analysis, Proc. of High
Performance Yacht Design Conference, Auckland, 2002.
10. Rulence-Paques, P., Fruchart E., Dru V., Mullet E. Cognitive Algebra in Sport Decision Making. Theory and Decision, 58, 387- 406., 2005
11. Saury, J. and Durand, M. Practical Knowledge in Expert Coaches: On-Site
Study of Coaching in
Sailing. Research Quarterly for Exercise and Sport, 69(3), 254-266, 1998.
12. Luce, R. D. And Raiffa, H., Games and Decisions: Introduction and Critical Survey, Wiley, New York, 1967
APPENDIX A – PAYOFF MATRICES Table 4 - payoff matrix for awaref = 25° and tws = 6m/s
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©2008: Royal Institution of Naval Architects
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